{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.lines import Line2D\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import warnings\n",
    "\n",
    "import bambi as bmb\n",
    "\n",
    "warnings.filterwarnings(\"ignore\", category=FutureWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ordinal Regression\n",
    "\n",
    "In some scenarios, the response variable is discrete, like a count, and ordered. Common examples of such data come from questionnaires where the respondent is asked to rate a product, service, or experience on a scale. This scale is often referred to as a [Likert scale](https://en.wikipedia.org/wiki/Likert_scale). For example, a five-level Likert scale could be:\n",
    "\n",
    "- 1 = Strongly disagree\n",
    "- 2 = Disagree\n",
    "- 3 = Neither agree nor disagree\n",
    "- 4 = Agree\n",
    "- 5 = Strongly agree\n",
    "\n",
    "The result is a set of **ordered categories** where each category has an associated numeric value (1-5). However, you can't compute a meaningful difference between the categories. Moreover, the response variable can also be a count where meaningful differences can be computed. For example, a restaurant can be rated on a scale of 1-5 stars where 1 is the worst and 5 is the best. Yes, you can compute the difference between 1 and 2 stars, but it is often treated as ordinal in an applied setting.\n",
    "\n",
    "Ordinal data presents three challenges when modelling:\n",
    "\n",
    "1. Unlike a count, the differences in the values are not necessarily equidistant or meaningful. For example, computing the difference between \"Strongly disagree\" and \"Disagree\". Or, in the case of the restaurant rating, it may be much harder for a restuarant to go from 4 to 5 stars than from 2 to 3 stars. \n",
    "2. The distribution of ordinal responses may be nonnormal as the response is not continuous; particularly if larger response levels are infrequently chosen compared to lower ones.\n",
    "3. The variances of the unobserved variables that underlie the observed ordered category may differ between the category, time points, etc. \n",
    "\n",
    "Thus, treating ordered categories as continuous is not appropriate. To this extent, Bambi supports two classes of ordinal regression models: (1) cumulative, and (2) sequential. Below, it is demonstrated how to fit these two models using Bambi to overcome the challenges of ordered category response data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cumulative model\n",
    "\n",
    "A cumulative model assumes that the observed ordinal variable $Y$ originates from the \"categorization\" of a latent continuous variable $Z$. To model the categorization process, the model assumes that there are $K$ thresholds (or cutpoints) $\\tau_k$ that partition $Z$ into $K+1$ observable, ordered categories of $Y$. The subscript $k$ in $\\tau_k$ is an index that associates that threshold to a particular category $k$. For example, if the response has three categories such as \"disagree\", \"neither agree nor disagree\", and \"agree\", then there are two thresholds $\\tau_1$ and $\\tau_2$ that partition $Z$ into $K+1 = 3$ categories. Additionally, if we assume $Z$ to have a certain distribution (e.g., Normal) with a cumulative distribution function $F$, the probability of $Y$ being equal to category $k$ is\n",
    "\n",
    "$$P(Y = k) = F(\\tau_k) - F(\\tau_{k-1})$$\n",
    "\n",
    "where $F(\\tau)$ is a cumulative probability. For example, suppose we are interested in the probability of each category stated above, and have two thresholds $\\tau_1 = -1, \\tau_2 = 1$ for the three categories. Additionally, if we assume $Z$ to be normally distributed with $\\sigma = 1$ and a cumulative distribution function $\\Phi$ then\n",
    "\n",
    "$$P(Y = 1) = \\Phi(\\tau_1) = \\Phi(-1)$$\n",
    "\n",
    "$$P(Y = 2) = \\Phi(\\tau_2) - \\Phi(\\tau_1) = \\Phi(1) - \\Phi(-1)$$\n",
    "\n",
    "$$P(Y = 3) = 1 - \\Phi(\\tau_2) = 1 - \\Phi(1)$$\n",
    "\n",
    "\n",
    "But how to set the values of the thresholds? By default, Bambi uses a Normal distribution with a grid of evenly spaced $\\mu$ that depends on the number of response levels as the prior for the thresholds. Additionally, since the thresholds need to be orderd, Bambi applies a transformation to the values such that the order is preserved. Furthermore, the model specification for ordinal regression typically transforms the cumulative probabilities using the log-cumulative-odds (logit) transformation. Therefore, the learned parameters for the thresholds $\\tau$ will be logits.\n",
    "\n",
    "Lastly, as each $F(\\tau)$ implies a cumulative probability for each category, the largest response level always has a cumulative probability of 1. Thus, we effectively do not need a parameter for it due to the law of total probability. For example, for three response values, we only need two thresholds as two thresholds partition $Z$ into $K+1$ categories."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The moral intuition dataset\n",
    "\n",
    "To illustrate an cumulative ordinal model, we will model data from a series of experiments conducted by philsophers (this example comes from Richard McElreath's [Statistical Rethinking](https://xcelab.net/rm/statistical-rethinking/)). The experiments aim to collect empirical evidence relevant to debates about moral intuition, the forms of reasoning through which people develop judgments about the moral goodness and badness of actions. \n",
    "\n",
    "In the dataset there are 12 columns and 9930 rows, comprising data for 331 unique individuals. The response we are interested in `response`, is an integer from 1 to 7 indicating how morally permissible the participant found the action to be taken (or not) in the story. The predictors are as follows:\n",
    "\n",
    "- `action`: a factor with levels 0 and 1 where 1 indicates that the story contained \"harm caused by action is morally worse than equivalent harm caused by omission\".\n",
    "- `intention`: a factor with levels 0 and 1 where 1 indicates that the story contained \"harm intended as the means to a goal is morally worse than equivalent harm foreseen as the side effect of a goal\".\n",
    "- `contact`: a factor with levels 0 and 1 where 1 indicates that the story contained \"using physical contact to cause harm to a victim is morally worse than causing equivalent harm to a victim without using physical contact\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "trolly = pd.read_csv(\"https://raw.githubusercontent.com/rmcelreath/rethinking/master/data/Trolley.csv\", sep=\";\")\n",
    "trolly = trolly[[\"response\", \"action\", \"intention\", \"contact\"]]\n",
    "trolly[\"action\"] = pd.Categorical(trolly[\"action\"], ordered=False)\n",
    "trolly[\"intention\"] = pd.Categorical(trolly[\"intention\"], ordered=False)\n",
    "trolly[\"contact\"] = pd.Categorical(trolly[\"contact\"], ordered=False)\n",
    "trolly[\"response\"] = pd.Categorical(trolly[\"response\"], ordered=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 3, 5, 2, 1, 7, 6]\n",
       "Categories (7, int64): [1 < 2 < 3 < 4 < 5 < 6 < 7]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 7 ordered categories from 1-7\n",
    "trolly.response.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Intercept only model\n",
    "\n",
    "Before we fit a model with predictors, let's attempt to recover the parameters of an ordinal model using only the thresholds to get a feel for the cumulative family. Traditionally, in Bambi if we wanted to recover the parameters of the likelihood, we would use an intercept only model and write the formula as `response ~ 1` where `1` indicates to include the intercept. However, in the case of ordinal regression, the thresholds \"take the place\" of the intercept. Thus, we can write the formula as `response ~ 0` to indicate that we do not want to include an intercept. To fit a cumulative ordinal model, we pass `family=\"cumulative\"`. To compare the thresholds only model, we compute the empirical log-cumulative-odds of the categories directly from the data below and generate a bar plot of the response probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_117147/1548491577.py:3: RuntimeWarning: invalid value encountered in log\n",
      "  logit_func = lambda x: np.log(x / (1 - x))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-1.91609116, -1.26660559, -0.718634  ,  0.24778573,  0.88986365,\n",
       "        1.76938091,         nan])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr_k = trolly.response.value_counts().sort_index().values / trolly.shape[0]\n",
    "cum_pr_k = np.cumsum(pr_k)\n",
    "logit_func = lambda x: np.log(x / (1 - x))\n",
    "cum_logit = logit_func(cum_pr_k)\n",
    "cum_logit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 3))\n",
    "plt.bar(np.arange(1, 8), pr_k)\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xlabel(\"Response\")\n",
    "plt.title(\"Empirical probability of each response category\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [threshold]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b541e7837edd4e128fe3428198840106",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tomas/anaconda3/envs/bambi-dev/lib/python3.11/site-packages/pytensor/compile/function/types.py:970: RuntimeWarning: invalid value encountered in add\n",
      "  self.vm()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 8 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
     ]
    }
   ],
   "source": [
    "model = bmb.Model(\"response ~ 0\", data=trolly, family=\"cumulative\")\n",
    "idata = model.fit(random_seed=1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, the components of the model are outputed. Notice how the thresholds are a grid of six values ranging from -2 to 2. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Formula: response ~ 0\n",
       "        Family: cumulative\n",
       "          Link: p = logit\n",
       "  Observations: 9930\n",
       "        Priors: \n",
       "    target = p\n",
       "        \n",
       "        \n",
       "        Auxiliary parameters\n",
       "            threshold ~ Normal(mu: [-2.  -1.2 -0.4  0.4  1.2  2. ], sigma: 1.0, transform: ordered)\n",
       "------\n",
       "* To see a plot of the priors call the .plot_priors() method.\n",
       "* To see a summary or plot of the posterior pass the object returned by .fit() to az.summary() or az.plot_trace()"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>threshold[0]</th>\n",
       "      <td>-1.917</td>\n",
       "      <td>0.030</td>\n",
       "      <td>-1.969</td>\n",
       "      <td>-1.859</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2293.0</td>\n",
       "      <td>1520.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[1]</th>\n",
       "      <td>-1.267</td>\n",
       "      <td>0.024</td>\n",
       "      <td>-1.314</td>\n",
       "      <td>-1.223</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2826.0</td>\n",
       "      <td>1286.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[2]</th>\n",
       "      <td>-0.718</td>\n",
       "      <td>0.021</td>\n",
       "      <td>-0.759</td>\n",
       "      <td>-0.679</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2621.0</td>\n",
       "      <td>2089.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[3]</th>\n",
       "      <td>0.248</td>\n",
       "      <td>0.020</td>\n",
       "      <td>0.211</td>\n",
       "      <td>0.286</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2491.0</td>\n",
       "      <td>1849.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[4]</th>\n",
       "      <td>0.891</td>\n",
       "      <td>0.022</td>\n",
       "      <td>0.850</td>\n",
       "      <td>0.931</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2334.0</td>\n",
       "      <td>1882.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[5]</th>\n",
       "      <td>1.771</td>\n",
       "      <td>0.028</td>\n",
       "      <td>1.719</td>\n",
       "      <td>1.822</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2352.0</td>\n",
       "      <td>1795.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "threshold[0] -1.917  0.030  -1.969   -1.859      0.001      0.0    2293.0   \n",
       "threshold[1] -1.267  0.024  -1.314   -1.223      0.000      0.0    2826.0   \n",
       "threshold[2] -0.718  0.021  -0.759   -0.679      0.000      0.0    2621.0   \n",
       "threshold[3]  0.248  0.020   0.211    0.286      0.000      0.0    2491.0   \n",
       "threshold[4]  0.891  0.022   0.850    0.931      0.000      0.0    2334.0   \n",
       "threshold[5]  1.771  0.028   1.719    1.822      0.001      0.0    2352.0   \n",
       "\n",
       "              ess_tail  r_hat  \n",
       "threshold[0]    1520.0    1.0  \n",
       "threshold[1]    1286.0    1.0  \n",
       "threshold[2]    2089.0    1.0  \n",
       "threshold[3]    1849.0    1.0  \n",
       "threshold[4]    1882.0    1.0  \n",
       "threshold[5]    1795.0    1.0  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Viewing the summary dataframe, we see a total of six  `response_threshold` coefficients. Why six? Remember, we get the last parameter for free. Since there are seven categories, we only need six cutpoints. The index (using zero based indexing) of the `response_threshold` indicates the category that the threshold is associated with. Comparing to the empirical log-cumulative-odds computation above, the mean of the posterior distribution for each category is close to the empirical value.\n",
    "\n",
    "As the the log cumulative link is used, we need to apply the inverse of the logit function to transform back to cumulative probabilities. Below, we plot the cumulative probabilities for each category. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "expit_func = lambda x: 1 / (1 + np.exp(-x))\n",
    "cumprobs = expit_func(idata.posterior.threshold).mean((\"chain\", \"draw\"))\n",
    "cumprobs = np.append(cumprobs, 1)\n",
    "\n",
    "plt.figure(figsize=(7, 3))\n",
    "plt.plot(sorted(trolly.response.unique()), cumprobs, marker='o')\n",
    "plt.ylabel(\"Cumulative probability\")\n",
    "plt.xlabel(\"Response category\")\n",
    "plt.title(\"Cumulative probabilities of response categories\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3))\n",
    "for i in range(6):\n",
    "    outcome = expit_func(idata.posterior.threshold).sel(threshold_dim=i).to_numpy().flatten()\n",
    "    ax.hist(outcome, bins=15, alpha=0.5, label=f\"Category: {i}\")\n",
    "ax.set_xlabel(\"Probability\")\n",
    "ax.set_ylabel(\"Count\")\n",
    "ax.set_title(\"Cumulative Probability by Category\")\n",
    "ax.legend(bbox_to_anchor=(1.04, 1), loc=\"upper left\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can take the derivative of the cumulative probabilities to get the posterior probabilities for each category. Notice how the posterior probabilities in the barplot below are close to the empirical probabilities in barplot above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# derivative\n",
    "ddx = np.diff(cumprobs)\n",
    "probs = np.insert(ddx, 0, cumprobs[0])\n",
    "\n",
    "plt.figure(figsize=(7, 3))\n",
    "plt.bar(sorted(trolly.response.unique()), probs)\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xlabel(\"Response category\")\n",
    "plt.title(\"Posterior Probability of each response category\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice in the plots above, the jump in probability from category 3 to 4. Additionally, the estimates of the coefficients is precise for each category. Now that we have an understanding how the cumulative link function is applied to produce ordered cumulative outcomes, we will add predictors to the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adding predictors\n",
    "\n",
    "In the cumulative model described above, adding predictors was explicitly left out. In this section, it is described how predictors are added to ordinal cumulative models. When adding predictor variables, what we would like is for any predictor, as it increases, predictions are moved progressively (increased) through the categories in sequence. A linear regression is formed for $Z$ by adding a predictor term $\\eta$\n",
    "\n",
    "$$\\eta = \\beta_1 x_1 + \\beta_2 x_2 + ... + \\beta_n x_n$$\n",
    "\n",
    "Notice how similar this looks to an ordinary linear model. However, there is no intercept or error term. This is because the intercept is replaced by the threshold $\\tau$ and the error term $\\epsilon$ is added separately to obtain\n",
    "\n",
    "$$Z = \\eta + \\epsilon$$ \n",
    "\n",
    "Putting the predictor term together with the thresholds and cumulative distribution function, we obtain the probability of $Y$ being equal to a category $k$ as\n",
    "\n",
    "$$Pr(Y = k | \\eta) = F(\\tau_k - \\eta) - F(\\tau_{k-1} - \\eta)$$\n",
    "\n",
    "The same predictor term $\\eta$ is subtracted from each threshold because if we decrease the log-cumulative-odds of every outcome value $k$ below the maximum, this shifts probability mass upwards towards higher outcome values. Thus, positive $\\beta$ values correspond to increasing $x$, which is associated with an increase in the mean response $Y$. The parameters to be estimated from the model are the thresholds $\\tau$ and the predictor terms $\\eta$ coefficients.  \n",
    "\n",
    "To add predictors for ordinal models in Bambi, we continue to use the formula interface."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [threshold, action, intention, contact, action:intention, contact:intention]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e9770346ce3e4ae19876e74050953637",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tomas/anaconda3/envs/bambi-dev/lib/python3.11/site-packages/pytensor/compile/function/types.py:970: RuntimeWarning: invalid value encountered in accumulate\n",
      "  self.vm()\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 93 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
     ]
    }
   ],
   "source": [
    "model = bmb.Model(\n",
    "    \"response ~ 0 + action + intention + contact + action:intention + contact:intention\", \n",
    "    data=trolly, \n",
    "    family=\"cumulative\"\n",
    ")\n",
    "idata = model.fit(random_seed=1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the summary dataframe below, we only select the predictor variables as the cutpoints are not of interest at the moment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>action[1]</th>\n",
       "      <td>-0.463</td>\n",
       "      <td>0.054</td>\n",
       "      <td>-0.564</td>\n",
       "      <td>-0.360</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1418.0</td>\n",
       "      <td>1691.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>intention[1]</th>\n",
       "      <td>-0.274</td>\n",
       "      <td>0.058</td>\n",
       "      <td>-0.380</td>\n",
       "      <td>-0.161</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1264.0</td>\n",
       "      <td>1446.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>contact[1]</th>\n",
       "      <td>-0.325</td>\n",
       "      <td>0.068</td>\n",
       "      <td>-0.445</td>\n",
       "      <td>-0.189</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1203.0</td>\n",
       "      <td>1310.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>action:intention[1, 1]</th>\n",
       "      <td>-0.455</td>\n",
       "      <td>0.081</td>\n",
       "      <td>-0.607</td>\n",
       "      <td>-0.303</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>1505.0</td>\n",
       "      <td>1625.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>contact:intention[1, 1]</th>\n",
       "      <td>-1.279</td>\n",
       "      <td>0.099</td>\n",
       "      <td>-1.473</td>\n",
       "      <td>-1.109</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1326.0</td>\n",
       "      <td>1456.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  \\\n",
       "action[1]               -0.463  0.054  -0.564   -0.360      0.001    0.001   \n",
       "intention[1]            -0.274  0.058  -0.380   -0.161      0.002    0.001   \n",
       "contact[1]              -0.325  0.068  -0.445   -0.189      0.002    0.001   \n",
       "action:intention[1, 1]  -0.455  0.081  -0.607   -0.303      0.002    0.001   \n",
       "contact:intention[1, 1] -1.279  0.099  -1.473   -1.109      0.003    0.002   \n",
       "\n",
       "                         ess_bulk  ess_tail  r_hat  \n",
       "action[1]                  1418.0    1691.0    1.0  \n",
       "intention[1]               1264.0    1446.0    1.0  \n",
       "contact[1]                 1203.0    1310.0    1.0  \n",
       "action:intention[1, 1]     1505.0    1625.0    1.0  \n",
       "contact:intention[1, 1]    1326.0    1456.0    1.0  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(\n",
    "    idata, \n",
    "    var_names=[\"action\", \"intention\", \"contact\", \n",
    "               \"action:intention\", \"contact:intention\"]\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distribution of the slopes are all negative indicating that each of these story features reduces the rating—the acceptability of the story. Below, a forest plot is used to make this insight more clear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(\n",
    "    idata,\n",
    "    combined=True,\n",
    "    var_names=[\"action\", \"intention\", \"contact\", \n",
    "               \"action:intention\", \"contact:intention\"],\n",
    "    figsize=(7, 3),\n",
    "    textsize=11\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we can plot the cumulative probability of each category. Compared to the same plot above, notice how most of the category probabilities have been shifted to the left. Additionally, there is more uncertainty for category 3, 4, and 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(7, 3))\n",
    "for i in range(6):\n",
    "    outcome = expit_func(idata.posterior.threshold).sel(threshold_dim=i).to_numpy().flatten()\n",
    "    ax.hist(outcome, bins=15, alpha=0.5, label=f\"Category: {i}\")\n",
    "ax.set_xlabel(\"Probability\")\n",
    "ax.set_ylabel(\"Count\")\n",
    "ax.set_title(\"Cumulative Probability by Category\")\n",
    "ax.legend(bbox_to_anchor=(1.04, 1), loc=\"upper left\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior predictive distribution\n",
    "\n",
    "To get a sense of how well the ordinal model fits the data, we can plot samples from the posterior predictive distribution. To plot the samples, a utility function is defined below to assist in the plotting of discrete values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def adjust_lightness(color, amount=0.5):\n",
    "    import matplotlib.colors as mc\n",
    "    import colorsys\n",
    "    try:\n",
    "        c = mc.cnames[color]\n",
    "    except:\n",
    "        c = color\n",
    "    c = colorsys.rgb_to_hls(*mc.to_rgb(c))\n",
    "    return colorsys.hls_to_rgb(c[0], c[1] * amount, c[2])\n",
    "\n",
    "def plot_ppc_discrete(idata, bins, ax):\n",
    "    \n",
    "    def add_discrete_bands(x, lower, upper, ax, **kwargs):\n",
    "        for i, (l, u) in enumerate(zip(lower, upper)):\n",
    "            s = slice(i, i + 2)\n",
    "            ax.fill_between(x[s], [l, l], [u, u], **kwargs)\n",
    "\n",
    "    var_name = list(idata.observed_data.data_vars)[0]\n",
    "    y_obs = idata.observed_data[var_name].to_numpy()\n",
    "    \n",
    "    counts_list = []\n",
    "    for draw_values in az.extract(idata, \"posterior_predictive\")[var_name].to_numpy().T:\n",
    "        counts, _ = np.histogram(draw_values, bins=bins)\n",
    "        counts_list.append(counts)\n",
    "    counts_arr = np.stack(counts_list)\n",
    "\n",
    "    qts_90 = np.quantile(counts_arr, (0.05, 0.95), axis=0)\n",
    "    qts_70 = np.quantile(counts_arr, (0.15, 0.85), axis=0)\n",
    "    qts_50 = np.quantile(counts_arr, (0.25, 0.75), axis=0)\n",
    "    qts_30 = np.quantile(counts_arr, (0.35, 0.65), axis=0)\n",
    "    median = np.quantile(counts_arr, 0.5, axis=0)\n",
    "\n",
    "    colors = [adjust_lightness(\"C0\", x) for x in [1.8, 1.6, 1.4, 1.2, 0.9]]\n",
    "\n",
    "    add_discrete_bands(bins, qts_90[0], qts_90[1], ax=ax, color=colors[0])\n",
    "    add_discrete_bands(bins, qts_70[0], qts_70[1], ax=ax, color=colors[1])\n",
    "    add_discrete_bands(bins, qts_50[0], qts_50[1], ax=ax, color=colors[2])\n",
    "    add_discrete_bands(bins, qts_30[0], qts_30[1], ax=ax, color=colors[3])\n",
    "\n",
    "    \n",
    "    ax.step(bins[:-1], median, color=colors[4], lw=2, where=\"post\")\n",
    "    ax.hist(y_obs, bins=bins, histtype=\"step\", lw=2, color=\"black\", align=\"mid\")\n",
    "    handles = [\n",
    "        Line2D([], [], label=\"Observed data\", color=\"black\", lw=2),\n",
    "        Line2D([], [], label=\"Posterior predictive median\", color=colors[4], lw=2)\n",
    "    ]\n",
    "    ax.legend(handles=handles)\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idata_pps = model.predict(idata=idata, kind=\"response\", inplace=False)\n",
    "\n",
    "bins = np.arange(7)\n",
    "fig, ax = plt.subplots(figsize=(7, 3))\n",
    "ax = plot_ppc_discrete(idata_pps, bins, ax)\n",
    "ax.set_xlabel(\"Response category\")\n",
    "ax.set_ylabel(\"Count\")\n",
    "ax.set_title(\"Cumulative model - Posterior Predictive Distribution\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sequential Model\n",
    "\n",
    "For some ordinal variables, the assumption of a **single** underlying continuous variable (as in cumulative models) may not be appropriate. If the response can be understood as being the result of a sequential process, such that a higher response category is possible only after all lower categories are achieved, then a sequential model may be more appropriate than a cumulative model.\n",
    "\n",
    "Sequential models assume that for **every** category $k$ there is a latent continuous variable $Z$ that determines the transition between categories $k$ and $k+1$. Now, a threshold $\\tau$ belongs to each latent process. If there are 3 categories, then there are 3 latent processes. If $Z_k$ is greater than the threshold $\\tau_k$, the sequential process continues, otherwise it stops at category $k$. As with the cumulative model, we assume a distribution for $Z_k$ with a cumulative distribution function $F$.\n",
    "\n",
    "As an example, lets suppose we are interested in modeling the probability a boxer makes it to round 3. This implies that the particular boxer in question survived round 1 $Z_1 > \\tau_1$ , 2 $Z_2 > \\tau_2$, and 3 $Z_3 > \\tau_3$. This can be written as \n",
    "\n",
    "$$Pr(Y = 3) = (1 - P(Z_1 \\leq \\tau_1)) * (1 - P(Z_2 \\leq \\tau_2)) * P(Z_3 \\leq \\tau_3)$$\n",
    "\n",
    "As in the cumulative model above, if we assume $Y$ to be normally distributed with the thresholds $\\tau_1 = -1, \\tau_2 = 0, \\tau_3 = 1$ and cumulative distribution function $\\Phi$ then\n",
    "\n",
    "$$Pr(Y = 3) = (1 - \\Phi(\\tau_1)) * (1 - \\Phi(\\tau_2)) * \\Phi(\\tau_3)$$\n",
    "\n",
    "To add predictors to this sequential model, we follow the same specification in the _Adding Predictors_ section above. Thus, the sequential model with predictor terms becomes\n",
    "\n",
    "$$P(Y = k) = F(\\tau_k - \\eta) * \\prod_{j=1}^{k-1}{(1 - F(\\tau_j - \\eta))}$$\n",
    "\n",
    "Thus, the probability that $Y$ is equal to category $k$ is equal to the probability that it did not fall in one of the former categories $1: k-1$ multiplied by the probability that the sequential process stopped at $k$ rather than continuing past it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Human resources attrition dataset\n",
    "\n",
    "To illustrate an sequential model with a stopping ratio link function, we will use data from the IBM human resources employee attrition and performance [dataset](https://www.kaggle.com/datasets/pavansubhasht/ibm-hr-analytics-attrition-dataset). The original dataset contains 1470 rows and 35 columns. However, our goal is to model the total working years of employees using age as a predictor. This data lends itself to a sequential model as the response, total working years, is a sequential process. In order to have 10 years of working experience, it is necessarily true that the employee had 9 years of working experience. Additionally, age is choosen as a predictor as it is positively correlated with total working years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>YearsAtCompany</th>\n",
       "      <th>Age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10</td>\n",
       "      <td>49</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>8</td>\n",
       "      <td>33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>7</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1</td>\n",
       "      <td>59</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  YearsAtCompany  Age\n",
       "1             10   49\n",
       "3              8   33\n",
       "4              2   27\n",
       "5              7   32\n",
       "6              1   59"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "attrition = pd.read_csv(\"data/hr_employee_attrition.tsv.txt\", sep=\"\\t\")\n",
    "attrition = attrition[attrition[\"Attrition\"] == \"No\"]\n",
    "attrition[\"YearsAtCompany\"] = pd.Categorical(attrition[\"YearsAtCompany\"], ordered=True)\n",
    "attrition[[\"YearsAtCompany\", \"Age\"]].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below, the empirical probabilities of the response categories are computed. Employees are most likely to stay at the company between 1 and 10 years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pr_k = attrition.YearsAtCompany.value_counts().sort_index().values / attrition.shape[0]\n",
    "\n",
    "plt.figure(figsize=(7, 3))\n",
    "plt.bar(np.arange(0, 36), pr_k)\n",
    "plt.xlabel(\"Response category\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.title(\"Empirical probability of each response category\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Default prior of thresholds\n",
    "\n",
    "Before we fit the sequential model, it's worth mentioning that the default priors for the thresholds in a sequential model are different than the cumulative model. In the cumulative model, the default prior for the thresholds is a Normal distribution with a grid of evenly spaced $\\mu$ where an ordered transformation is applied to ensure the ordering of the values. However, in the sequential model, the ordering of the thresholds does not matter. Thus, the default prior for the thresholds is a Normal distribution with a zero $\\mu$ vector of length $k - 1$ where $k$ is the number of response levels. Refer to the [getting started](https://bambinos.github.io/bambi/notebooks/getting_started.html#specifying-priors) docs if you need a refresher on priors in Bambi. \n",
    "\n",
    "Subsequently, fitting a sequential model is similar to fitting a cumulative model. The only difference is that we pass `family=\"sratio\"` to the `bambi.Model` constructor. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [threshold, TotalWorkingYears]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "4f54440683794514b86bd0ef57029e8c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">\n",
       "</pre>\n"
      ],
      "text/plain": [
       "\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 370 seconds.\n",
      "We recommend running at least 4 chains for robust computation of convergence diagnostics\n"
     ]
    }
   ],
   "source": [
    "sequence_model = bmb.Model(\n",
    "    \"YearsAtCompany ~ 0 + TotalWorkingYears\", \n",
    "    data=attrition, \n",
    "    family=\"sratio\"\n",
    ")\n",
    "sequence_idata = sequence_model.fit(random_seed=1234)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "       Formula: YearsAtCompany ~ 0 + TotalWorkingYears\n",
       "        Family: sratio\n",
       "          Link: p = logit\n",
       "  Observations: 1233\n",
       "        Priors: \n",
       "    target = p\n",
       "        Common-level effects\n",
       "            TotalWorkingYears ~ Normal(mu: 0.0, sigma: 0.3223)\n",
       "        \n",
       "        Auxiliary parameters\n",
       "            threshold ~ Normal(mu: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
       "             0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.], sigma: 1.0)\n",
       "------\n",
       "* To see a plot of the priors call the .plot_priors() method.\n",
       "* To see a summary or plot of the posterior pass the object returned by .fit() to az.summary() or az.plot_trace()"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sequence_model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>TotalWorkingYears</th>\n",
       "      <td>0.127</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.117</td>\n",
       "      <td>0.138</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>458.0</td>\n",
       "      <td>719.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[0]</th>\n",
       "      <td>-2.518</td>\n",
       "      <td>0.188</td>\n",
       "      <td>-2.849</td>\n",
       "      <td>-2.154</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>2139.0</td>\n",
       "      <td>893.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[1]</th>\n",
       "      <td>-1.051</td>\n",
       "      <td>0.106</td>\n",
       "      <td>-1.253</td>\n",
       "      <td>-0.861</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1668.0</td>\n",
       "      <td>1416.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[2]</th>\n",
       "      <td>-1.014</td>\n",
       "      <td>0.117</td>\n",
       "      <td>-1.237</td>\n",
       "      <td>-0.806</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1480.0</td>\n",
       "      <td>1458.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[3]</th>\n",
       "      <td>-0.757</td>\n",
       "      <td>0.113</td>\n",
       "      <td>-0.973</td>\n",
       "      <td>-0.554</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1200.0</td>\n",
       "      <td>1390.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[4]</th>\n",
       "      <td>-0.759</td>\n",
       "      <td>0.122</td>\n",
       "      <td>-0.978</td>\n",
       "      <td>-0.521</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1394.0</td>\n",
       "      <td>1346.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[5]</th>\n",
       "      <td>0.250</td>\n",
       "      <td>0.108</td>\n",
       "      <td>0.060</td>\n",
       "      <td>0.458</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1069.0</td>\n",
       "      <td>1283.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[6]</th>\n",
       "      <td>-0.505</td>\n",
       "      <td>0.148</td>\n",
       "      <td>-0.790</td>\n",
       "      <td>-0.228</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1436.0</td>\n",
       "      <td>1496.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[7]</th>\n",
       "      <td>-0.085</td>\n",
       "      <td>0.138</td>\n",
       "      <td>-0.338</td>\n",
       "      <td>0.171</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1373.0</td>\n",
       "      <td>1364.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[8]</th>\n",
       "      <td>0.028</td>\n",
       "      <td>0.143</td>\n",
       "      <td>-0.228</td>\n",
       "      <td>0.305</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.003</td>\n",
       "      <td>980.0</td>\n",
       "      <td>1503.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[9]</th>\n",
       "      <td>0.388</td>\n",
       "      <td>0.151</td>\n",
       "      <td>0.101</td>\n",
       "      <td>0.662</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.003</td>\n",
       "      <td>1306.0</td>\n",
       "      <td>1373.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[10]</th>\n",
       "      <td>1.269</td>\n",
       "      <td>0.153</td>\n",
       "      <td>0.948</td>\n",
       "      <td>1.523</td>\n",
       "      <td>0.005</td>\n",
       "      <td>0.004</td>\n",
       "      <td>801.0</td>\n",
       "      <td>1164.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[11]</th>\n",
       "      <td>0.440</td>\n",
       "      <td>0.218</td>\n",
       "      <td>0.061</td>\n",
       "      <td>0.871</td>\n",
       "      <td>0.006</td>\n",
       "      <td>0.004</td>\n",
       "      <td>1224.0</td>\n",
       "      <td>1354.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[12]</th>\n",
       "      <td>-0.105</td>\n",
       "      <td>0.297</td>\n",
       "      <td>-0.643</td>\n",
       "      <td>0.454</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1733.0</td>\n",
       "      <td>1697.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[13]</th>\n",
       "      <td>0.517</td>\n",
       "      <td>0.242</td>\n",
       "      <td>0.084</td>\n",
       "      <td>0.992</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1361.0</td>\n",
       "      <td>1272.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[14]</th>\n",
       "      <td>0.390</td>\n",
       "      <td>0.280</td>\n",
       "      <td>-0.151</td>\n",
       "      <td>0.910</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1730.0</td>\n",
       "      <td>1358.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[15]</th>\n",
       "      <td>0.797</td>\n",
       "      <td>0.264</td>\n",
       "      <td>0.289</td>\n",
       "      <td>1.273</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>1632.0</td>\n",
       "      <td>1534.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[16]</th>\n",
       "      <td>0.426</td>\n",
       "      <td>0.335</td>\n",
       "      <td>-0.193</td>\n",
       "      <td>1.066</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1787.0</td>\n",
       "      <td>1330.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[17]</th>\n",
       "      <td>0.249</td>\n",
       "      <td>0.372</td>\n",
       "      <td>-0.444</td>\n",
       "      <td>0.944</td>\n",
       "      <td>0.010</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1390.0</td>\n",
       "      <td>1357.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[18]</th>\n",
       "      <td>0.794</td>\n",
       "      <td>0.335</td>\n",
       "      <td>0.180</td>\n",
       "      <td>1.423</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1591.0</td>\n",
       "      <td>1638.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[19]</th>\n",
       "      <td>0.793</td>\n",
       "      <td>0.370</td>\n",
       "      <td>0.110</td>\n",
       "      <td>1.499</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1689.0</td>\n",
       "      <td>1201.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[20]</th>\n",
       "      <td>2.201</td>\n",
       "      <td>0.272</td>\n",
       "      <td>1.723</td>\n",
       "      <td>2.725</td>\n",
       "      <td>0.008</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1133.0</td>\n",
       "      <td>1333.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[21]</th>\n",
       "      <td>1.842</td>\n",
       "      <td>0.349</td>\n",
       "      <td>1.177</td>\n",
       "      <td>2.449</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.007</td>\n",
       "      <td>1388.0</td>\n",
       "      <td>1316.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[22]</th>\n",
       "      <td>2.444</td>\n",
       "      <td>0.342</td>\n",
       "      <td>1.762</td>\n",
       "      <td>3.046</td>\n",
       "      <td>0.009</td>\n",
       "      <td>0.006</td>\n",
       "      <td>1544.0</td>\n",
       "      <td>1429.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[23]</th>\n",
       "      <td>0.030</td>\n",
       "      <td>0.724</td>\n",
       "      <td>-1.373</td>\n",
       "      <td>1.291</td>\n",
       "      <td>0.013</td>\n",
       "      <td>0.016</td>\n",
       "      <td>3182.0</td>\n",
       "      <td>1571.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[24]</th>\n",
       "      <td>1.587</td>\n",
       "      <td>0.538</td>\n",
       "      <td>0.516</td>\n",
       "      <td>2.535</td>\n",
       "      <td>0.013</td>\n",
       "      <td>0.009</td>\n",
       "      <td>1902.0</td>\n",
       "      <td>1429.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[25]</th>\n",
       "      <td>1.507</td>\n",
       "      <td>0.597</td>\n",
       "      <td>0.292</td>\n",
       "      <td>2.507</td>\n",
       "      <td>0.011</td>\n",
       "      <td>0.008</td>\n",
       "      <td>2841.0</td>\n",
       "      <td>1557.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[26]</th>\n",
       "      <td>1.735</td>\n",
       "      <td>0.632</td>\n",
       "      <td>0.582</td>\n",
       "      <td>2.871</td>\n",
       "      <td>0.012</td>\n",
       "      <td>0.008</td>\n",
       "      <td>3066.0</td>\n",
       "      <td>1220.0</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[27]</th>\n",
       "      <td>1.047</td>\n",
       "      <td>0.749</td>\n",
       "      <td>-0.325</td>\n",
       "      <td>2.439</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.010</td>\n",
       "      <td>2780.0</td>\n",
       "      <td>1363.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[28]</th>\n",
       "      <td>1.156</td>\n",
       "      <td>0.755</td>\n",
       "      <td>-0.300</td>\n",
       "      <td>2.467</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.010</td>\n",
       "      <td>2965.0</td>\n",
       "      <td>1382.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[29]</th>\n",
       "      <td>0.543</td>\n",
       "      <td>0.850</td>\n",
       "      <td>-1.078</td>\n",
       "      <td>2.144</td>\n",
       "      <td>0.016</td>\n",
       "      <td>0.016</td>\n",
       "      <td>2806.0</td>\n",
       "      <td>1360.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[30]</th>\n",
       "      <td>1.268</td>\n",
       "      <td>0.788</td>\n",
       "      <td>-0.124</td>\n",
       "      <td>2.844</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.012</td>\n",
       "      <td>3180.0</td>\n",
       "      <td>1638.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[31]</th>\n",
       "      <td>1.373</td>\n",
       "      <td>0.781</td>\n",
       "      <td>-0.118</td>\n",
       "      <td>2.799</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.011</td>\n",
       "      <td>2961.0</td>\n",
       "      <td>1629.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[32]</th>\n",
       "      <td>2.653</td>\n",
       "      <td>0.732</td>\n",
       "      <td>1.315</td>\n",
       "      <td>4.084</td>\n",
       "      <td>0.015</td>\n",
       "      <td>0.011</td>\n",
       "      <td>2384.0</td>\n",
       "      <td>1292.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[33]</th>\n",
       "      <td>0.861</td>\n",
       "      <td>0.942</td>\n",
       "      <td>-0.994</td>\n",
       "      <td>2.554</td>\n",
       "      <td>0.014</td>\n",
       "      <td>0.016</td>\n",
       "      <td>4345.0</td>\n",
       "      <td>1567.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>threshold[34]</th>\n",
       "      <td>1.757</td>\n",
       "      <td>0.892</td>\n",
       "      <td>0.128</td>\n",
       "      <td>3.399</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.013</td>\n",
       "      <td>2441.0</td>\n",
       "      <td>1202.0</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  \\\n",
       "TotalWorkingYears  0.127  0.006   0.117    0.138      0.000    0.000   \n",
       "threshold[0]      -2.518  0.188  -2.849   -2.154      0.004    0.003   \n",
       "threshold[1]      -1.051  0.106  -1.253   -0.861      0.003    0.002   \n",
       "threshold[2]      -1.014  0.117  -1.237   -0.806      0.003    0.002   \n",
       "threshold[3]      -0.757  0.113  -0.973   -0.554      0.003    0.002   \n",
       "threshold[4]      -0.759  0.122  -0.978   -0.521      0.003    0.002   \n",
       "threshold[5]       0.250  0.108   0.060    0.458      0.003    0.002   \n",
       "threshold[6]      -0.505  0.148  -0.790   -0.228      0.004    0.003   \n",
       "threshold[7]      -0.085  0.138  -0.338    0.171      0.004    0.003   \n",
       "threshold[8]       0.028  0.143  -0.228    0.305      0.005    0.003   \n",
       "threshold[9]       0.388  0.151   0.101    0.662      0.004    0.003   \n",
       "threshold[10]      1.269  0.153   0.948    1.523      0.005    0.004   \n",
       "threshold[11]      0.440  0.218   0.061    0.871      0.006    0.004   \n",
       "threshold[12]     -0.105  0.297  -0.643    0.454      0.007    0.006   \n",
       "threshold[13]      0.517  0.242   0.084    0.992      0.007    0.005   \n",
       "threshold[14]      0.390  0.280  -0.151    0.910      0.007    0.005   \n",
       "threshold[15]      0.797  0.264   0.289    1.273      0.007    0.005   \n",
       "threshold[16]      0.426  0.335  -0.193    1.066      0.008    0.006   \n",
       "threshold[17]      0.249  0.372  -0.444    0.944      0.010    0.007   \n",
       "threshold[18]      0.794  0.335   0.180    1.423      0.008    0.006   \n",
       "threshold[19]      0.793  0.370   0.110    1.499      0.009    0.007   \n",
       "threshold[20]      2.201  0.272   1.723    2.725      0.008    0.006   \n",
       "threshold[21]      1.842  0.349   1.177    2.449      0.009    0.007   \n",
       "threshold[22]      2.444  0.342   1.762    3.046      0.009    0.006   \n",
       "threshold[23]      0.030  0.724  -1.373    1.291      0.013    0.016   \n",
       "threshold[24]      1.587  0.538   0.516    2.535      0.013    0.009   \n",
       "threshold[25]      1.507  0.597   0.292    2.507      0.011    0.008   \n",
       "threshold[26]      1.735  0.632   0.582    2.871      0.012    0.008   \n",
       "threshold[27]      1.047  0.749  -0.325    2.439      0.014    0.010   \n",
       "threshold[28]      1.156  0.755  -0.300    2.467      0.014    0.010   \n",
       "threshold[29]      0.543  0.850  -1.078    2.144      0.016    0.016   \n",
       "threshold[30]      1.268  0.788  -0.124    2.844      0.014    0.012   \n",
       "threshold[31]      1.373  0.781  -0.118    2.799      0.014    0.011   \n",
       "threshold[32]      2.653  0.732   1.315    4.084      0.015    0.011   \n",
       "threshold[33]      0.861  0.942  -0.994    2.554      0.014    0.016   \n",
       "threshold[34]      1.757  0.892   0.128    3.399      0.018    0.013   \n",
       "\n",
       "                   ess_bulk  ess_tail  r_hat  \n",
       "TotalWorkingYears     458.0     719.0   1.00  \n",
       "threshold[0]         2139.0     893.0   1.00  \n",
       "threshold[1]         1668.0    1416.0   1.00  \n",
       "threshold[2]         1480.0    1458.0   1.00  \n",
       "threshold[3]         1200.0    1390.0   1.00  \n",
       "threshold[4]         1394.0    1346.0   1.00  \n",
       "threshold[5]         1069.0    1283.0   1.00  \n",
       "threshold[6]         1436.0    1496.0   1.00  \n",
       "threshold[7]         1373.0    1364.0   1.00  \n",
       "threshold[8]          980.0    1503.0   1.00  \n",
       "threshold[9]         1306.0    1373.0   1.00  \n",
       "threshold[10]         801.0    1164.0   1.00  \n",
       "threshold[11]        1224.0    1354.0   1.00  \n",
       "threshold[12]        1733.0    1697.0   1.00  \n",
       "threshold[13]        1361.0    1272.0   1.00  \n",
       "threshold[14]        1730.0    1358.0   1.00  \n",
       "threshold[15]        1632.0    1534.0   1.00  \n",
       "threshold[16]        1787.0    1330.0   1.00  \n",
       "threshold[17]        1390.0    1357.0   1.00  \n",
       "threshold[18]        1591.0    1638.0   1.00  \n",
       "threshold[19]        1689.0    1201.0   1.00  \n",
       "threshold[20]        1133.0    1333.0   1.00  \n",
       "threshold[21]        1388.0    1316.0   1.00  \n",
       "threshold[22]        1544.0    1429.0   1.00  \n",
       "threshold[23]        3182.0    1571.0   1.00  \n",
       "threshold[24]        1902.0    1429.0   1.00  \n",
       "threshold[25]        2841.0    1557.0   1.00  \n",
       "threshold[26]        3066.0    1220.0   1.01  \n",
       "threshold[27]        2780.0    1363.0   1.00  \n",
       "threshold[28]        2965.0    1382.0   1.00  \n",
       "threshold[29]        2806.0    1360.0   1.00  \n",
       "threshold[30]        3180.0    1638.0   1.00  \n",
       "threshold[31]        2961.0    1629.0   1.00  \n",
       "threshold[32]        2384.0    1292.0   1.00  \n",
       "threshold[33]        4345.0    1567.0   1.00  \n",
       "threshold[34]        2441.0    1202.0   1.00  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(sequence_idata)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The coefficients are still on the logits scale, so we need to apply the inverse of the logit function to transform back to probabilities. Below, we plot the probabilities for each category."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "probs = expit_func(sequence_idata.posterior.threshold).mean((\"chain\", \"draw\"))\n",
    "probs = np.append(probs, 1)\n",
    "\n",
    "plt.figure(figsize=(7, 3))\n",
    "plt.plot(sorted(attrition.YearsAtCompany.unique()), probs, marker='o')\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.xlabel(\"Response category\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot can seem confusing at first. Remember, the sequential model is a product of probabilities, i.e., the probability that $Y$ is equal to category $k$ is equal to the probability that it did not fall in one of the former categories $1: k-1$ multiplied by the probability that the sequential process stopped at $k$. Thus, the probability of category 5 is the probability that the sequential process did not fall in 0, 1, 2, 3, or 4 multiplied by the probability that the sequential process stopped at 5. This makes sense why the probability of category 36 is 1. There is no category after 36, so once you multiply all of the previous probabilities with the current category, you get 1. This is the reason for the \"cumulative-like\" shape of the plot. But if the coefficients were truly cumulative, the probability could not decreases as $k$ increases. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Posterior predictive samples\n",
    "\n",
    "Again, using the posterior predictive samples, we can visualize the model fit against the observed data. In the case of the sequential model, the model does an alright job of capturing the observed frequencies of the categories. For pedagogical purposes, this fit is sufficient."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZU2mTMfz9/WFvb682srZnzx7cuXNH7bR0ZfftwoQQZaZp2bIlzpw5gzFjxmDPnj1IT0+v8H48PDxQv379cqcv6Xu44H18UY4cOYLMzMwifd3Z2RmdOnUq0tdlMhl69uypts7Dw0Pj7+v/Op5mpRJ5eXnBy8sLwNMh76lTp2LRokUIDw9HeHg47t69CwB47bXXis1fcIojNTUVwNMflcLs7e01mrpesO/Jkydj8uTJxaYp/GNtZWWl9rrglGNmZmaF9w8AEydOxNdff42pU6fC19cXFhYW0NHRwYgRIzQuEwAsLS3VXisUilLXP3nyBCYmJkhNTYWenl6R0xwymQz29vbS+1DS+6Gnp1ekje7evYvt27eXeJq9IgERAHTu3FntRzIoKKjMW7YYGhrizz//BPD0PXNxcVGbpZeamlrszFNHR0dpOwAEBgYiNzcXq1atwptvvon8/Hy89tpr+PTTT9G1a9dS61DQ3956660S09y/f1/tFFd5ZvEV1K24tI6OjkV+uDSZGRgVFQWlUgm5XA4nJ6ci73FJ5d69exdXrlwp870v6HeFyy3u815YSkoKAFTqpBA9PT0EBgZi6dKlePDgAczNzbFmzRo4ODjAz89PSlfZfbuwgveuoB8WZ9q0aTA2Nsb69euxYsUK6Orqon379vjiiy+k796yVLRPlPQ9fObMmQqVU1Fl9fXIyEi1dUZGRmp/cABPP/8v4pZE/wUM5qhc5HI5QkNDsWjRIulaloJreX7++ecSrwkB/j+ISkpKKrKt8LqCD2/hi1wLf7EW7HvatGno27dvsfvV9Jq18iq4hmru3Llq6+/du1ehWwhUFisrK+Tm5iIlJUUtoBNCICkpSQq6n30/np0JmpubK33hFrC2toaHhwc+++yzYvdZ2g9VcVauXKl2Xd6z14OVREdHp9QfNisrKyQmJhZZXzC55dl9DB06FEOHDkVGRgb+/PNPhIaGIiAgAP/++2+pfbigjKVLl5Y4q9nOzk7tdXlGmgrei8TExCIBzZ07d4q0jyajV82aNSuznYsr19raGoaGhvj++++LzVNQZkG/S01NVQvoivu8F1bQTwtP9nheQ4cOxfz586VraH///XeMHz8eurq6avWvzL5d2O+//w6ZTIb27duXmEZPTw8TJ07ExIkT8eDBA0RFRWH69Onw8/PDzZs3yzWjuKJ9oqTv4WffOwMDA6hUqiLpnifAfbavF1ZcX6eKYTBHRSQmJhb711PBqcOCLzk/Pz/o6enh6tWrpZ5Scnd3h4ODA3788UdMnDhR+vK5fv06oqOj1b40C0ZYzp49q/ZX9O+//16kTDc3N5w5c6ZIMPU89PX1yz2qVnAT22ft3LkTt2/fRr169SqtTuXVuXNnhIeHY/369ZgwYYK0/pdffkFGRoZ0gX7BLLUNGzagRYsWUrqffvqpyCy+gIAA7Nq1C6+88gosLCyeu44vIsDu3Lkz5s2bh5MnT0qTFgDghx9+gEwmQ8eOHYvkMTY2hr+/P7Kzs9GnTx9cuHABLi4uJY7WtmnTBubm5rh48SLGjh1baXUvOLW5fv16tRHu48ePIy4uDjNmzKi0fVVUQEAA5s6dCysrK7i6upaYrmPHjggPD8eGDRsQEhIird+4cWOZ+/Dx8YFSqcSKFSvwzjvvlBiYPPu+GBoallluw4YN0apVK0RERCAvLw9ZWVkYOnRokeOrzL79rIiICPzxxx8YOHAgateuXa485ubmeOutt3D79m2MHz8eCQkJaNSo0XOfQSispO/hIUOGSGnq1KmDLVu2ICsrS9p/amoqoqOj1UbFK1I3b29vGBoaYv369dKsceBpIL9///5SR72pbAzmqAg/Pz84OTmhZ8+eaNCgAfLz83H69GksWLAAJiYm+OCDDwA8/cB/8sknmDFjBq5du4bu3bvDwsICd+/exbFjx2BsbCzNKJszZw5GjBiBN954AyNHjsSDBw8QFhZWZMjf3t4eXbp0wbx582BhYQEXFxfs27cPW7duLVLPlStXwt/fH35+fggODkatWrVw//59xMXF4eTJk9iyZUuFj71p06bYtGkTNm/ejLp168LAwABNmzYtNm1AQADWrFmDBg0awMPDA7GxsZg/f36lnjKqiK5du8LPzw9Tp05Feno62rRpI81m9fT0RGBgIICnP3SDBw/G4sWLIZfL0aVLF5w/fx5ffvllkZuMfvLJJ4iMjISPjw9CQkLg7u6OJ0+eICEhAbt27cKKFSuq7HgLTJgwAT/88AN69OiBTz75BC4uLti5cyeWL1+O0aNHS9cTjRw5EoaGhmjTpg0cHByQlJSEefPmQalUSoFUkyZNAADffvstTE1NYWBgAFdXV1hZWWHp0qUICgrC/fv38dZbb8HW1hYpKSk4c+YMUlJS8M0331S47u7u7hg1ahSWLl0KHR0d6R56M2fOhLOzs1pQ/rKNHz8ev/zyC9q3b48JEybAw8MD+fn5uHHjBvbu3YtJkyahVatW6NatG9q3b48pU6YgIyMDXl5e+Pvvv7Fu3boy92FiYoIFCxZgxIgR6NKlC0aOHAk7OztcuXIFZ86cwbJlywBA+gx+8cUX8Pf3h66uLjw8PKRLDYozbNgwvPvuu7hz5w58fHyK/CFRGX07MzMTMTEx0v+vXbuGX3/9FTt27JBm55amZ8+eaNKkCby8vGBjY4Pr169j8eLFcHFxkWZ2Fhz7kiVLEBQUBLlcDnd3d5iampZadkmSk5Ol72GVSoXQ0FAYGBhg2rRpUprAwECsXLkSgwcPxsiRI5Gamorw8PAi3w+mpqZwcXHBb7/9hs6dO8PS0hLW1tbFXvZgbm6OmTNnYvr06RgyZAgGDBiA1NRUzJ49GwYGBggNDdXoeOh/qngCBlVDmzdvFgMHDhRubm7CxMREyOVyUbt2bREYGCguXrxYJP2vv/4qOnbsKMzMzIS+vr5wcXERb731loiKilJL99133wk3NzehUChE/fr1xffff19kdpQQQiQmJoq33npLWFpaCqVSKQYPHixOnDhR7IzQM2fOiH79+glbW1shl8uFvb296NSpk1ixYoWUpmBWVeFZecXNnE1ISBDdunUTpqamAoBUt+JmpKalpYnhw4cLW1tbYWRkJNq2bSsOHz5cZCZYRWezbtmyRW19SfUvmK2YkpIircvMzBRTp04VLi4uQi6XCwcHBzF69GiRlpamljcrK0tMmjRJ2NraCgMDA9G6dWtx5MiRIjPghHg6Yy0kJES4uroKuVwuLC0tRYsWLcSMGTPEo0ePpHR4gbNZy3L9+nUxcOBAYWVlJeRyuXB3dxfz58+XZjQLIcTatWtFx44dhZ2dnVAoFMLR0VH069dPnD17Vq2sxYsXC1dXV6Grq1vkfTt06JDo0aOHsLS0FHK5XNSqVUv06NFD7T0r7n0pvO1ZeXl54osvvhD169cXcrlcWFtbi8GDB4ubN2+qpStr9mRJ+yquHuUt99GjR+Ljjz8W7u7uQqFQCKVSKZo2bSomTJggkpKSpHQPHjwQw4YNE+bm5sLIyEh07dpV/PPPP2XOZi2wa9cu4evrK4yNjYWRkZFo1KiR2izQrKwsMWLECGFjYyNkMplaGcX1WSGEUKlUwtDQUAAQq1atKvb4ytu3S2o3/G/GPwBhbGws6tatK9566y2xZcsWtb5XoHBdFyxYIHx8fIS1tbVQKBSidu3aYvjw4SIhIUEt37Rp04Sjo6PQ0dFR+85ycXERPXr0KLZ+Jc1mXbdunQgJCRE2NjZCX19ftGvXTpw4caJI/rVr14qGDRsKAwMD0ahRI7F58+Ziv6+joqKEp6en0NfXV5sNX9J7/d133wkPDw+pP/Xu3bvIzOGSPvfFfX7oKZkQ5ZhyQ/SCBAcH4+DBg3x+HxERkYZ4axIiIiIiLcZgjoiIiEiL8TQrERERkRbjyBwRERGRFmMwR0RERKTFGMwRERERabEqvWnwvHnzsHXrVvzzzz8wNDSEj48PvvjiC7WbOwYHB2Pt2rVq+Vq1aiXdqBF4+uinyZMn48cff0RmZiY6d+6M5cuXq93wMS0tDSEhIdKTBHr16oWlS5eW+7FL+fn5uHPnDkxNTSvtgdBERERExRFC4OHDh3B0dJSedV5a4irj5+cnIiIixPnz58Xp06dFjx49RO3atdVu1hgUFCS6d+8uEhMTpSU1NVWtnPfee0/UqlVLREZGipMnT4qOHTuKZs2aidzcXClN9+7dRZMmTUR0dLSIjo4WTZo0EQEBAeWu682bN9VuEMmFCxcuXLhw4fKil8I3EC9OtZrNmpKSAltbWxw6dEh6OHFwcDAePHiAX3/9tdg8KpUKNjY2WLduHfr37w/g6UN7nZ2dsWvXLvj5+SEuLg6NGjVCTEwMWrVqBQCIiYmBt7c3/vnnn3I9L1KlUsHc3Bw3b94s8kgTIiIiosqUnp4OZ2dnPHjwAEqlstS01erZrCqVCgBgaWmptv7gwYOwtbWFubk5fH198dlnn8HW1hYAEBsbi5ycHHTr1k1K7+joiCZNmiA6Ohp+fn44cuQIlEqlFMgBQOvWraFUKhEdHV1sMJeVlYWsrCzp9cOHDwEAZmZmDOaIiIjopSjPpV3VZgKEEAITJ05E27ZtpYddA4C/vz82bNiA/fv3Y8GCBTh+/Dg6deokBVpJSUlQKBSwsLBQK8/Ozg5JSUlSmoLg71m2trZSmsIKHsBdsDg7O1fWoRIRERFVmmozMjd27FicPXsWf/31l9r6glOnANCkSRN4eXnBxcUFO3fuRN++fUssTwihFs0WF9kWTvOsadOmYeLEidLrguFOIiIiouqkWozMjRs3Dr///jsOHDigNgO1OA4ODnBxccHly5cBAPb29sjOzkZaWppauuTkZNjZ2Ulp7t69W6SslJQUKU1h+vr60ilVnlolIiKi6qpKR+aEEBg3bhy2bduGgwcPwtXVtcw8qampuHnzJhwcHAAALVq0gFwuR2RkJPr16wcASExMxPnz5xEeHg4A8Pb2hkqlwrFjx9CyZUsAwNGjR6FSqeDj4/OCjo6I6OXIy8tDTk5OVVeDiCpILpdDV1f3ucup0tmsY8aMwcaNG/Hbb7+pTUJQKpUwNDTEo0ePEBYWhjfffBMODg5ISEjA9OnTcePGDcTFxcHU1BQAMHr0aOzYsQNr1qyBpaUlJk+ejNTUVMTGxkqN5O/vjzt37mDlypUAgFGjRsHFxQXbt28vV13T09OhVCqhUqk4SkdE1cajR49w69YtVKMbExBROclkMjg5OcHExKTItorEHVUazJV0vVpERASCg4ORmZmJPn364NSpU3jw4AEcHBzQsWNHzJkzR+36tSdPnuDDDz/Exo0b1W4a/Gya+/fvF7lp8LJly8p902AGc0RU3eTl5eHy5cswMjKCjY0Nb2hOpEWEEEhJScHjx4/h5uZWZIROa4I5bcJgjoiqmydPniA+Ph516tSBoaFhVVeHiCooMzMTCQkJcHV1hYGBgdq2isQd1WY2K2mftMw85ORV/G8Bua4MFobPf40AET3FETki7VRZn10Gc6SRtMw8/HD6gcb5h7xqzoCOiIioElSLW5OQ9tFkRK4y8xMREdFTDOZIY9l5Ak9y8yu8ZDOQI6JyqlOnDhYvXlzV1ag0mhxPcHAw+vTp80LqQ/8NDOZII6mPc3FDlYNb6bkVXm6ocpD6OLeqD4GIqtDNmzcxfPhwODo6QqFQwMXFBR988AFSU1OrumpaLyEhATKZDKdPn67qqtBLwmCONJKdJ5CdV/FRuacjcxydI6rJrl27Bi8vL/z777/48ccfceXKFaxYsQL79u2Dt7c37t+/X2V1y8vLQ35+fpXtn0gTDOZII/cycnHjQQ5uqSq+3HiQg3sZHJkjqqnef/99KBQK7N27F76+vqhduzb8/f0RFRWF27dvY8aMGWrpHz58iIEDB8LExASOjo5YunSp2vawsDDUrl0b+vr6cHR0REhIiLQtOzsbU6ZMQa1atWBsbIxWrVrh4MGD0vY1a9bA3NwcO3bsQKNGjaCvr49Vq1bBwMAADx48UNtPSEgIfH19pdfR0dFo3749DA0N4ezsjJCQEGRkZEjbk5OT0bNnTxgaGsLV1RUbNmwos23y8vIwceJEmJubw8rKClOmTClyQ+jdu3ejbdu2UpqAgABcvXpV2l7wNCVPT0/IZDJ06NABAHD8+HF07doV1tbWUCqV8PX1xcmTJ8usE1V/nM1KGsn638icJncplMme5ieiyufl5YWkpKSXvl97e3ucOHGizHT379/Hnj178NlnnxW5N569vT0GDRqEzZs3Y/ny5dJtG+bPn4/p06cjLCwMe/bswYQJE9CgQQN07doVP//8MxYtWoRNmzahcePGSEpKwpkzZ6Qyhw4dioSEBGzatAmOjo7Ytm0bunfvjnPnzsHNzQ0A8PjxY8ybNw/fffcdrKys4OTkhNDQUPzyyy8YPnw4gKdB1k8//YRPPvkEAHDu3Dn4+flhzpw5WL16NVJSUjB27FiMHTsWERERAJ5e63bz5k3s378fCoUCISEhSE5OLrV9FixYgO+//x6rV69Go0aNsGDBAmzbtg2dOnWS0mRkZGDixIlo2rQpMjIyMGvWLLzxxhs4ffo0dHR0pEdXRkVFoXHjxlAoFACeBsVBQUH46quvpH29/vrruHz5svREJdJSgspFpVIJAEKlUlV1VaqFOg2bCT2lncZLnYbNqvoQiLReZmamuHjxosjMzJTW1apVSwB46UutWrXKVeeYmBgBQGzbtq3Y7QsXLhQAxN27d4UQQri4uIju3burpenfv7/w9/cXQgixYMECUb9+fZGdnV2krCtXrgiZTCZu376ttr5z585i2rRpQgghIiIiBABx+vRptTQhISGiU6dO0us9e/YIhUIh7t+/L4QQIjAwUIwaNUotz+HDh4WOjo7IzMwUly5dEgBETEyMtD0uLk4AEIsWLSqpeYSDg4P4/PPPpdc5OTnCyclJ9O7du8Q8ycnJAoA4d+6cEEKI+Ph4AUCcOnWqxDxCCJGbmytMTU3F9u3bS01HL05xn+ECFYk7ODJHGkm5m4hcVel/YZbmni5H5oheBHt7e63er/jfcP+zN1P19vZWS+Pt7S3NCH377bexePFi1K1bF927d8frr7+Onj17Qk9PDydPnoQQAvXr11fLn5WVBSsrK+m1QqGAh4eHWppBgwbB29sbd+7cgaOjIzZs2IDXX38dFhYWAIDY2FhcuXJF7dSpEAL5+fmIj4/Hv//+Cz09PXh5eUnbGzRoUOojJFUqFRITE9WOt6AM8cxpkKtXr2LmzJmIiYnBvXv3pGv8bty4gSZNmpRYfnJyMmbNmoX9+/fj7t27yMvLw+PHj3Hjxo0S85B2YDBHGsnO+d81bzIZdI3My50v7/EDQAhk5fCaOaIXoTynOqtSvXr1IJPJcPHixWJvt/HPP//AwsIC1tbWpZZTEOw5Ozvj0qVLiIyMRFRUFMaMGYP58+fj0KFDyM/Ph66uLmJjY4s89/LZB5sbGhoWuRN/y5Yt8corr2DTpk0YPXo0tm3bJp0+BYD8/Hy8++67atfnFahduzYuXbqkVs/K1LNnTzg7O2PVqlVwdHREfn4+mjRpguzs7FLzBQcHIyUlBYsXL4aLiwv09fXh7e1dZj6q/hjMkUYK/kjUNTKHw/Dl5c6XuHoM8jLSNLrWjoi0n5WVFbp27Yrly5djwoQJatfNJSUlYcOGDRgyZIhaEBQTE6NWRkxMDBo0aCC9NjQ0RK9evdCrVy+8//77aNCgAc6dOwdPT0/k5eUhOTkZ7dq1q3BdBw4ciA0bNsDJyQk6Ojro0aOHtK158+a4cOEC6tWrV2zehg0bIjc3FydOnEDLli0BAJcuXSoyqeJZSqUSDg4OiImJQfv27QEAubm5iI2NRfPmzQEAqampiIuLw8qVK6Vj+uuvv9TKKbhGLi8vT2394cOHsXz5crz++usAnt4e5t69e+VtDqrGGMzRc5LB0NWzQumJqGZbtmwZfHx84Ofnh08//RSurq64cOECPvzwQ9SqVQufffaZWvq///4b4eHh6NOnDyIjI7Flyxbs3LkTwNPZqHl5eWjVqhWMjIywbt06GBoawsXFBVZWVhg0aBCGDBmCBQsWwNPTE/fu3cP+/fvRtGlTKagpyaBBgzB79mx89tlneOutt9QehD516lS0bt0a77//PkaOHAljY2PExcUhMjISS5cuhbu7O7p3746RI0fi22+/hZ6eHsaPH19k0kdhH3zwAT7//HO4ubmhYcOGWLhwoVoAaGFhASsrK3z77bdwcHDAjRs38NFHH6mVYWtrC0NDQ+zevRtOTk4wMDCAUqlEvXr1sG7dOnh5eSE9PR0ffvhhmfUh7cBbk9DzkQFOZvJyL4zliMjNzQ0nTpzAK6+8gv79++OVV17BqFGj0LFjRxw5cgSWlpZq6SdNmoTY2Fh4enpizpw5WLBgAfz8/AAA5ubmWLVqFdq0aQMPDw/s27cP27dvl66Ji4iIwJAhQzBp0iS4u7ujV69eOHr0KJydnctVz9deew1nz57FoEGD1LZ5eHjg0KFDuHz5Mtq1awdPT0/MnDkTDg4OUpqIiAg4OzvD19cXffv2xahRo2Bra1vqPidNmoQhQ4YgODgY3t7eMDU1xRtvvCFt19HRwaZNmxAbG4smTZpgwoQJmD9/vloZenp6+Oqrr7By5Uo4Ojqid+/eAIDvv/8eaWlp8PT0RGBgIEJCQsqsD2kHmRA84VUe6enpUCqVUKlUMDMzq+rqVDmFmRVyHt6Hroklhq4/W+58EYM9kPfoPuSmlshO553eiZ7HkydPEB8fD1dXV7VRIyLSDqV9hisSd/A0Kz03Az0O8BIREVUVBnP0XGQAnMzK3414lpWIiKhyMZij58aROSIioqrDX2EiIiIiLcZgjoiIiEiL8TQrPReZDBjQVFnu9B/yojkiIqJKxWCOnputCbsRERFRVeFpViIiIiItxmCOiIiISIsxmCMiIirBmjVrYG5uXtXVqBQymQy//vorACAhIQEymQynT5/WuLzKKKM6KXw8Bw8ehEwmU3s2bnXFYI6IiF6q4OBgyGQyyGQyyOVy1K1bF5MnT0ZGRsZzl13ZAUb//v3x77//VkpZ1YmzszMSExPRpEmTcqUPDg5Gnz59nqsMbePj44PExEQoleWf5FdVeOU6ERG9dN27d0dERARycnJw+PBhjBgxAhkZGfjmm2+qumqSnJwcGBoawtDQ8LnLkcvllVanyihLV1cX9vb2VV5GdaZQKLTm+DgyR0REL52+vj7s7e3h7OyMgQMHYtCgQdIpwKysLISEhMDW1hYGBgZo27Ytjh8/LuVNS0vDoEGDYGNjA0NDQ7i5uSEiIgIA4OrqCgDw9PSETCZDhw4dpHwRERFo2LAhDAwM0KBBAyxfvlzaVjCi99NPP6FDhw4wMDDA+vXriz3N+s033+CVV16BQqGAu7s71q1bp7ZdJpNhxYoV6N27N4yNjfHpp58W2wZ16tTBnDlzMHDgQJiYmMDR0RFLly4tV1nbt29HixYtYGBggLp162L27NnIzc2V8l2+fBnt27eHgYEBGjVqhMjISLVyixvBvHDhAnr06AEzMzOYmpqiXbt2uHr1KsLCwrB27Vr89ttv0ojqwYMH1crIz8+Hk5MTVqxYobafkydPQiaT4dq1awAAlUqFUaNGwdbWFmZmZujUqRPOnDlTbPsUfl/atWsHQ0NDvPbaa/j3339x/PhxeHl5wcTEBN27d0dKSopa3tLebwA4duwYPD09YWBgAC8vL5w6dUpte+HTrKmpqRgwYACcnJxgZGSEpk2b4scff1TL06FDB4SEhGDKlCmwtLSEvb09wsLCSjy+ysKROSKi/5DXv9iJlIdPXvp+bUwNsGtqD43zGxoaIicnBwAwZcoU/PLLL1i7di1cXFwQHh4OPz8/XLlyBZaWlpg5cyYuXryIP/74A9bW1rhy5QoyMzMBPP2BbtmyJaKiotC4cWMoFAoAwKpVqxAaGoply5bB09MTp06dwsiRI2FsbIygoCCpHlOnTsWCBQsQEREBfX197N27V62e27ZtwwcffIDFixejS5cu2LFjB4YOHQonJyd07NhRShcaGop58+Zh0aJF0NXVLfG458+fj+nTpyMsLAx79uzBhAkT0KBBA3Tt2rXEsvbs2YPBgwfjq6++kgKuUaNGSWnz8/PRt29fWFtbIyYmBunp6Rg/fnyp7X/79m20b98eHTp0wP79+2FmZoa///4bubm5mDx5MuLi4pCeni4FzZaWlrhz546UX0dHB++88w42bNiA9957T1q/ceNGeHt7o27duhBCoEePHrC0tMSuXbugVCqxcuVKdO7cGf/++y8sLS1LrF9oaCgWL16M2rVrY9iwYRgwYADMzMywZMkSGBkZoV+/fpg1a5Y0slvW+52RkYGAgAB06tQJ69evR3x8PD744INS2+jJkydo0aIFpk6dCjMzM+zcuROBgYGoW7cuWrVqJaVbu3YtJk6ciKNHj+LIkSMIDg5GmzZt1N7TysZgjojoPyTl4RMkPXhc1dWokGPHjmHjxo3o3LmzdKp1zZo18Pf3B/D0hzkyMhKrV6/Ghx9+iBs3bsDT0xNeXl4Ano5wFbCxsQEAWFlZqZ0imzNnDhYsWIC+ffsCeDqCd/HiRaxcuVItmBs/fryUpjhffvklgoODMWbMGADAxIkTERMTgy+//FItmBs4cCCGDRtW5rG3adMGH330EQCgfv36+Pvvv7Fo0SK1H/7CZQUGBuKjjz6S6l23bl3MmTMHU6ZMQWhoKKKiohAXF4eEhAQ4OTkBAObOnSu1Z3G+/vprKJVKbNq0STqNW79+fWm7oaEhsrKySj3tOGjQICxcuBDXr1+Hi4sL8vPzsWnTJkyfPh0AcODAAZw7dw7JycnQ19eX2vPXX3/Fzz//LAWkxZk8eTL8/PwAAB988AEGDBiAffv2oU2bNgCA4cOHY82aNVL6st7vDRs2IC8vD99//z2MjIzQuHFj3Lp1C6NHjy6xDrVq1cLkyZOl1+PGjcPu3buxZcsWtWDOw8MDoaGhAAA3NzcsW7YM+/btYzBHRETlY2NqoBX73bFjB0xMTJCbm4ucnBz07t0bS5cuxdWrV5GTkyP9SAOAXC5Hy5YtERcXBwAYPXo03nzzTZw8eRLdunVDnz594OPjU+K+UlJScPPmTQwfPhwjR46U1ufm5ha5uL0gQCxJXFxckaCjTZs2WLJkSYXKKeDt7V3k9eLFi0stKzY2FsePH8dnn30mrcvLy8OTJ0/w+PFjxMXFoXbt2lIgV9x+Cjt9+jTatWv3XNfjeXp6okGDBvjxxx/x0Ucf4dChQ0hOTka/fv2kej969AhWVlZq+TIzM3H16tVSy/bw8JD+b2dnBwBo2rSp2rrk5GQA5Xu/4+Li0KxZMxgZGUnby2qjvLw8fP7559i8eTNu376NrKwsZGVlwdjYuMS6AoCDg4NUtxeFwRwR0X/I85zqfJk6duyIb775BnK5HI6OjlIQkZiYCODptWLPEkJI6/z9/XH9+nXs3LkTUVFR6Ny5M95//318+eWXxe4rPz8fwNMRvmdHUAAUOQVa+Ie5OKXVrSLllLf8wmXl5+dj9uzZxY4gGhgYQAhRZpmFPe8kjwKDBg3Cxo0b8dFHH2Hjxo3w8/ODtbW1VG8HBwccPHiwSL6ybv/ybJBZcCyF1xW8z+V5v4tro7IsWLAAixYtwuLFi9G0aVMYGxtj/PjxyM7OLrGuhev2onACBBERvXTGxsaoV68eXFxc1H786tWrB4VCgb/++ktal5OTgxMnTqBhw4bSOhsbGwQHB2P9+vVYvHgxvv32WwCQrpHLy8uT0trZ2aFWrVq4du0a6tWrp7YUTJgor4YNG6rVDQCio6PV6lYRMTExRV43aNCg1DzNmzfHpUuXihxLvXr1oKOjg0aNGuHGjRtq17QdOXKk1DI9PDxw+PBh6brFwhQKhVqblmTgwIE4d+4cYmNj8fPPP2PQoEFq9U5KSoKenl6RehcEfJWhPO93o0aNcObMGelaS6Doe1HY4cOH0bt3bwwePBjNmjVD3bp1cfny5Uqr9/PgyBwREVUbxsbGGD16ND788ENYWlqidu3aCA8Px+PHjzF8+HAAwKxZs9CiRQs0btwYWVlZ2LFjhxRM2drawtDQELt374aTkxMMDAygVCoRFhaGkJAQmJmZwd/fH1lZWThx4gTS0tIwceLEctfvww8/RL9+/dC8eXN07twZ27dvx9atWxEVFaXR8f79998IDw9Hnz59EBkZiS1btmDnzp2l5pk1axYCAgLg7OyMt99+Gzo6Ojh79izOnTuHTz/9FF26dIG7uzuGDBmCBQsWID09HTNmzCi1zLFjx2Lp0qV45513MG3aNCiVSsTExKBly5Zwd3dHnTp1sGfPHly6dAlWVlYl3nvN1dUVPj4+GD58OHJzc9G7d29pW5cuXeDt7Y0+ffrgiy++gLu7O+7cuYNdu3ahT58+5T41XR5lvd8DBw7EjBkzMHz4cHz88cdISEgocWS3QL169fDLL78gOjoaFhYWWLhwIZKSkjQO5CsTR+aIiKha+fzzz/Hmm28iMDAQzZs3x5UrV7Bnzx5YWFgAeDpKNG3aNHh4eKB9+/bQ1dXFpk2bAAB6enr46quvsHLlSjg6OkrBxIgRI/Ddd99hzZo1aNq0KXx9fbFmzZoKj8z16dMHS5Yswfz589G4cWOsXLkSERERardAqYhJkyYhNjYWnp6e0kX7BRf6l8TPzw87duxAZGQkXnvtNbRu3RoLFy6Ei4sLgKczS7dt24asrCy0bNkSI0aMULu+rjhWVlbYv38/Hj16BF9fX7Ro0QKrVq2SRk1HjhwJd3d3eHl5wcbGBn///XeJZQ0aNAhnzpxB37591U7fymQy7Nq1C+3bt8ewYcNQv359vPPOO0hISJCug6ssZb3fJiYm2L59Oy5evAhPT0/MmDEDX3zxRallzpw5E82bN4efnx86dOgAe3v7IjdSrjKiCs2dO1d4eXkJExMTYWNjI3r37i3++ecftTT5+fkiNDRUODg4CAMDA+Hr6yvOnz+vlubJkydi7NixwsrKShgZGYmePXuKmzdvqqW5f/++GDx4sDAzMxNmZmZi8ODBIi0trdx1ValUAoBQqVQaH+9/idzUUgAQclPLl5KPiIrKzMwUFy9eFJmZmVVdFdKAi4uLWLRoUVVXg6pQaZ/hisQdVToyd+jQIbz//vuIiYlBZGQkcnNz0a1bN7VHuoSHh2PhwoVYtmwZjh8/Dnt7e3Tt2hUPHz6U0owfPx7btm3Dpk2b8Ndff+HRo0cICAhQO78/cOBAnD59Grt378bu3btx+vRpBAYGvtTjJSIiIqpsVXrN3O7du9VeR0REwNbWFrGxsWjfvj2EEFi8eDFmzJghzdpZu3Yt7OzssHHjRrz77rtQqVRYvXo11q1bhy5dugAA1q9fD2dnZ0RFRcHPzw9xcXHYvXs3YmJipJktq1atgre3Ny5dugR3d/eXe+BERERElaRaXTOnUqkAQLoLdHx8PJKSktCtWzcpjb6+Pnx9fREdHQ3g6X1rcnJy1NI4OjqiSZMmUpojR45AqVSqTVFu3bo1lEqllKawrKwspKenqy1ERESVJSEhocwnMxCVR7UJ5oQQmDhxItq2bYsmTZoAAJKSkgCgyIWRdnZ20rakpCQoFArpwtiS0tja2hbZp62trZSmsHnz5kGpVEqLs7Pz8x0gERER0QtQbYK5sWPH4uzZs0UeWguU7waNhRVOU1z60sqZNm0aVCqVtNy8ebM8h0FE9NIJDW6ASkRVr7I+u9UimBs3bhx+//13HDhwQO3xIwXPgCs8epacnCyN1tnb2yM7OxtpaWmlprl7926R/aakpJQ4HVpfXx9mZmZqCxFRdVJwN/vCd6AnIu1Q8Nkt/CSSiqrSCRBCCIwbNw7btm3DwYMHi9zvx9XVFfb29oiMjISnpyeApwd+6NAh6X4wLVq0gFwuR2RkpPT8t8TERJw/fx7h4eEAnj5vTaVS4dixY2jZsiUA4OjRo1CpVKU+z4+IqDrT09ODkZERUlJSIJfLoaNTLf4+J6JyyM/PR0pKCoyMjKCn93zhWJUGc++//z42btyI3377DaamptIInFKphKGhIWQyGcaPH4+5c+fCzc0Nbm5umDt3LoyMjDBw4EAp7fDhwzFp0iRYWVnB0tISkydPRtOmTaXZrQ0bNkT37t0xcuRIrFy5EgAwatQoBAQEcCYrEWktmUwGBwcHxMfH4/r161VdHSKqIB0dHdSuXbvMS8fKUqXB3DfffAMARe6cHRERgeDgYADAlClTkJmZiTFjxiAtLQ2tWrXC3r17YWpqKqVftGgR9PT00K9fP2RmZqJz585Ys2aN2rDlhg0bEBISIs167dWrF5YtW/ZiD5CI6AVTKBRwc3PjqVYiLaRQKCplRF0meOVsuaSnp0OpVEKlUvH6OQAKMyvkPLwPuaklstNTX3g+IiKimqQicQcvsCAiIiLSYgzmiIiIiLQYgzkiIiIiLcZgjoiIiEiLMZgjIiIi0mIM5oiIiIi0GIM5IiIiIi3GYI6IiIhIizGYIyIiItJiDOaIiIiItBiDOSIiIiItxmCOiIiISIsxmCMiIiLSYgzmiIiIiLQYgzkiIiIiLcZgjoiIiEiLMZgjIiIi0mIM5oiIiIi0GIM5IiIiIi3GYI6IiIhIizGYIyIiItJiDOaIiIiItBiDOSIiIiItxmCOiIiISIsxmCMiIiLSYgzmiIiIiLQYgzkiIiIiLcZgjoiIiEiLMZgjIiIi0mIM5oiIiIi0GIM5IiIiIi3GYI6IiIhIizGYIyIiItJiDOaIiIiItFiVBnN//vknevbsCUdHR8hkMvz6669q24ODgyGTydSW1q1bq6XJysrCuHHjYG1tDWNjY/Tq1Qu3bt1SS5OWlobAwEAolUoolUoEBgbiwYMHL/joiIiIiF48varceUZGBpo1a4ahQ4fizTffLDZN9+7dERERIb1WKBRq28ePH4/t27dj06ZNsLKywqRJkxAQEIDY2Fjo6uoCAAYOHIhbt25h9+7dAIBRo0YhMDAQ27dvf0FHRuWR/Ci3wnnkujJYGOpWOF9aZh5y8kSF8z3PPomIiF6GKg3m/P394e/vX2oafX192NvbF7tNpVJh9erVWLduHbp06QIAWL9+PZydnREVFQU/Pz/ExcVh9+7diImJQatWrQAAq1atgre3Ny5dugR3d/fKPSgqFyGAH8+pNMrbo74JzPTLH1w9zMrDjn8fabSvAkNeNWdAR0RE1VKVBnPlcfDgQdja2sLc3By+vr747LPPYGtrCwCIjY1FTk4OunXrJqV3dHREkyZNEB0dDT8/Pxw5cgRKpVIK5ACgdevWUCqViI6OLjGYy8rKQlZWlvQ6PT39BR0hVdTO5wzMNKHpqB4REdGLVq2DOX9/f7z99ttwcXFBfHw8Zs6ciU6dOiE2Nhb6+vpISkqCQqGAhYWFWj47OzskJSUBAJKSkqTg71m2trZSmuLMmzcPs2fPrtwDIjVPcvMrnEdHJoNCV1bhfNl5AvlCs4BMR1bx/REREb0s1TqY69+/v/T/Jk2awMvLCy4uLti5cyf69u1bYj4hBGTP/ADLivkxLpymsGnTpmHixInS6/T0dDg7O1f0EKgEAsCt9IpfMwcA9iZ60KvA1J2cPIG7GXka7atA6uNc2JpU648LERHVUFr16+Tg4AAXFxdcvnwZAGBvb4/s7GykpaWpjc4lJyfDx8dHSnP37t0iZaWkpMDOzq7Efenr60NfX7+Sj4CepdnIHJCkwcSJ7Lx85Gt4plRH9nRkj4iIqDrSKJirW7cujh8/DisrK7X1Dx48QPPmzXHt2rVKqVxhqampuHnzJhwcHAAALVq0gFwuR2RkJPr16wcASExMxPnz5xEeHg4A8Pb2hkqlwrFjx9CyZUsAwNGjR6FSqaSAj16egjOdeRlpWDfUS6MyTCxt8MaCP8qdPidP4KYqGxqeZYVMBtzL0GwUkYiI6EXTKJhLSEhAXl7R01ZZWVm4fft2uct59OgRrly5Ir2Oj4/H6dOnYWlpCUtLS4SFheHNN9+Eg4MDEhISMH36dFhbW+ONN94AACiVSgwfPhyTJk2ClZUVLC0tMXnyZDRt2lSa3dqwYUN0794dI0eOxMqVKwE8vTVJQEAAZ7JWJSGQlVbyNYulyUpLqlAgKITQeFSuwDVHe8RfPP18hRAREb0AFQrmfv/9d+n/e/bsgVKplF7n5eVh3759qFOnTrnLO3HiBDp27Ci9LrhGLSgoCN988w3OnTuHH374AQ8ePICDgwM6duyIzZs3w9TUVMqzaNEi6OnpoV+/fsjMzETnzp2xZs0a6R5zALBhwwaEhIRIs1579eqFZcuWVeTQqZLoGZtDSENkFZtYkJdxX/q/poGgpu7p8jQrERFVTzIhyn/ySUfn6VXnMpkMhbPJ5XLUqVMHCxYsQEBAQOXWshpIT0+HUqmESqWCmZlZVVenyinMrJDz8D7kppbITk8td75XZ2xFqipDo33e/WkW8h9rdm86TeU9fgAIUeHjJCIieh4ViTsqNDKXn//0gnVXV1ccP34c1tbWmteSaqQOr9bH1ug4iPyKzy61GzDvBdSodImrxyAvI03j6+2IiIheNI2umYuPj6/selAN4fmKI3bdlld1NSqA95gjIqLqTeNbk+zbtw/79u1DcnKyNGJX4Pvvv3/uitF/k5OZHM5KucYjXbn5Ano6FQ+wNM13jbEcERFVcxoFc7Nnz8Ynn3wCLy8vODg4lHrzXaJnWRvroZ6VvsazS/PyBXQ1CMo0zffn//5lFycioupKo2BuxYoVWLNmDQIDAyu7PjVaWmaexs8AlevKtOJB8ApdGRS6FXh8QyWq6JMjAJ5kJSKi6k+jYC47O5s33K1kaZl5+OH0g+cqY8ir5tU+oLMy0kNtpVzj56Tm5QOaxIKaPtOViIioutMomBsxYgQ2btyImTNnVnZ9aixNR+Qqu4wXTa5bEFQxsCIiIqoMGgVzT548wbfffouoqCh4eHhALlefnbhw4cJKqVxNk50nNB6x0tGSi7osDHUx5FVzjQLPh1l52PHvI4333aO+Ccz0KzZy+aF2NCsREdVgGgVzZ8+exauvvgoAOH/+vNo2TobQTOrjXNxQ5Tx3GbYmGk9Qfmk0PRVsa6KHIa/qaRQIass1hURERBWl0S//gQMHKrseNV52nkB2Xr7Gszx1ZE/L+K9jQEZERKSu+g/j1BD3MnJxJTVL4/uvyWRPyyAiIqKaRaNgrmPHjqWeTt2/f7/GFaqpbqXn4OZznma9lf58+YmIiEj7aBTMFVwvVyAnJwenT5/G+fPnERQUVBn1qnG+/u0wMh9kapxfpqOLU1cbIqi5ZSXWioiIiKo7jYK5RYsWFbs+LCwMjx5pPtuwJju3ciJyHqU9VxnfbrLE4revVFKNiIiISBtU6jVzgwcPRsuWLfHll19WZrE1Qt5jFfIyni+Yy+FMYiIiohqnUoO5I0eOwMDAoDKLrDGURvq49xCATAf65rYVypv14C40njlBREREWk2jYK5v375qr4UQSExMxIkTJ/hUCA3p/O8RVUaWthi4+kSF8kYM9kDeo/t8GDwREVENpFEwp1Qq1V7r6OjA3d0dn3zyCbp161YpFatpZNK/MhhU9GnwREREVGNpFMxFRERUdj1qvILHcenqAE5mFXtbOCBHRERUcz3XNXOxsbGIi4uDTCZDo0aN4OnpWVn1qrFkAEfmiIiIqNw0CuaSk5Pxzjvv4ODBgzA3N4cQAiqVCh07dsSmTZtgY2NT2fX8z9P53/CakVwHA5oqS09cCB8GT0REVHNpNAQ0btw4pKen48KFC7h//z7S0tJw/vx5pKenIyQkpLLrWKPoyJ4+UL4iCxEREdVcGkUCu3fvRlRUFBo2bCita9SoEb7++mtOgCAiIiJ6iTQK5vLz8yGXy4usl8vlyM/Pf+5K0cuTlpmHnDzeo46IiEhbaRTMderUCR988AF+/PFHODo6AgBu376NCRMmoHPnzpVaQXpx0jLz8MPpBxrl5T2KiYiIqgeNgrlly5ahd+/eqFOnDpydnSGTyXDjxg00bdoU69evr+w60guSkyeQnSeQz8iMiIhIa2kUzDk7O+PkyZOIjIzEP//8AyEEGjVqhC5dulR2/egFSn2cixuqHI3yMvwjIiKqHioUzO3fvx9jx45FTEwMzMzM0LVrV3Tt2hUAoFKp0LhxY6xYsQLt2rV7IZWlypWdJ5Cdl498RmZERERaq0LB3OLFizFy5EiYmZkV2aZUKvHuu+9i4cKFDOa0xL2MXFxJzXqu6994hpaIiKhqVSiYO3PmDL744osSt3fr1g1ffvnlc1eKXo5b6Tm4qeFpVp5nJSIiqh4qFMzdvXu32FuSSIXp6SElJeW5K0Uvx8krd/DkehxEfp4GuRnNERERVQcVCuZq1aqFc+fOoV69esVuP3v2LBwcHCqlYvTirfqgD7If3tcob97jBwAAGR8lRkREVKUqFMy9/vrrmDVrFvz9/WFgYKC2LTMzE6GhoQgICKjUCtKLk/MoDXkZac9Vhn4pI7VERET04lUomPv444+xdetW1K9fH2PHjoW7uztkMhni4uLw9ddfIy8vDzNmzHhRdaUXRSaDvrmdRlkdHTkSS0REVJUqFMzZ2dkhOjoao0ePxrRp0yD+N5VRJpPBz88Py5cvh52dZkEBvXwFp0h1jS0QGHGiwvl1ZMCY1ywruVZERERUEToVzeDi4oJdu3bh3r17OHr0KGJiYnDv3j3s2rULderUqVBZf/75J3r27AlHR0fIZDL8+uuvatuFEAgLC4OjoyMMDQ3RoUMHXLhwQS1NVlYWxo0bB2traxgbG6NXr164deuWWpq0tDQEBgZCqVRCqVQiMDAQDx48qOih/6cZ6OlUeFHo6kChy4vmiIiIqlKFg7kCFhYWeO2119CyZUtYWFhoVEZGRgaaNWuGZcuWFbs9PDwcCxcuxLJly3D8+HHY29uja9euePjwoZRm/Pjx2LZtGzZt2oS//voLjx49QkBAAPLy/n+G5sCBA3H69Gns3r0bu3fvxunTpxEYGKhRnf+LZACczPQqvNRWymFlpNFDRIiIiKiSVOkvsb+/P/z9/YvdJoTA4sWLMWPGDPTt2xcAsHbtWtjZ2WHjxo149913oVKpsHr1aqxbt056lNj69evh7OyMqKgo+Pn5IS4uDrt370ZMTAxatWoFAFi1ahW8vb1x6dIluLu7v5yDreYM9DSL6+UcmSMiIqpS1XZYJT4+HklJSejWrZu0Tl9fH76+voiOjsa7776L2NhY5OTkqKVxdHREkyZNEB0dDT8/Pxw5cgRKpVIK5ACgdevWUCqViI6OLjGYy8rKQlZWlvQ6PT39BRxl9SCTAQOaKiucT64rg4Wh7guoEREREZVXtQ3mkpKSAKDIhAo7Oztcv35dSqNQKIqc5rWzs5PyJyUlwdbWtkj5tra2UprizJs3D7Nnz36uY6gKyY9yNcpna1JtuwIRERGVotr/gssK3ZVWCFFkXWGF0xSXvqxypk2bhokTJ0qv09PT4ezsXN5qVwkhgB/PqSqUnoiIiLRbtQ3m7O3tATwdWXv2qRLJycnSaJ29vT2ys7ORlpamNjqXnJwMHx8fKc3du3eLlJ+SklLqbVT09fWhr69fKcfyMj3Jza/qKhAREdFLpPFs1hfN1dUV9vb2iIyMlNZlZ2fj0KFDUqDWokULyOVytTSJiYk4f/68lMbb2xsqlQrHjh2T0hw9ehQqlUpK818hAFy5n13uhQNzRERE2q9KR+YePXqEK1euSK/j4+Nx+vRpWFpaonbt2hg/fjzmzp0LNzc3uLm5Ye7cuTAyMsLAgQMBAEqlEsOHD8ekSZNgZWUFS0tLTJ48GU2bNpVmtzZs2BDdu3fHyJEjsXLlSgDAqFGjEBAQ8J+Zyfrs6dKrqVklJyxHfiIiItIuVRrMnThxAh07dpReF1yjFhQUhDVr1mDKlCnIzMzEmDFjkJaWhlatWmHv3r0wNTWV8ixatAh6enro168fMjMz0blzZ6xZswa6uv8/y3LDhg0ICQmRZr326tWrxHvbaTUB3ErPqVB6IiIi0m4yITguUx7p6elQKpVQqVQwMzOr9PKdnJxw+/Zt1KpVq8gTLMoiN7VC7qP70DW2gMPw5eXOl7h6DPIy0qBnYomch6kVrXKNoDCzQs7D+5CbWiI7nW1EREQvR0Xijmo7AYLKr2BSbt7jB0hcPabc+fIeP1DLT0RERNqHwdx/gL5cjhwAEAJ5GWka5SciIiLtxGDuP8DR0RHXhebDa46ODmUnIiIiomqJwdx/wK/7orE4JhX5Glz9qCMDxre2qvxKERER0UvBYO4/wMpID/Us9ZGvwVwWHZkMVkbsBkRERNqKv+L/EQpdGQDOZCAiIqppqu0TIKj85LrPF8Q9b34iIiKqOhyZ+w+wMNTFkFfNkZNX8dOscl0ZLAx1y05IRERE1RKDuf8IBmREREQ1E0+zEhEREWkxBnNEREREWozBHBEREZEWYzBHREREpMUYzBERERFpMQZzRERERFqMwRwRERGRFmMwR0RERKTFGMwRERERaTEGc0RERERajMEcERERkRZjMEdERESkxRjMEREREWkxBnNEREREWozBHBEREZEWYzBHREREpMUYzBERERFpMQZzRERERFqMwRwRERGRFmMwR0RERKTFGMwRERERaTEGc0RERERajMEcERERkRZjMEdERESkxRjMEREREWmxah3MhYWFQSaTqS329vbSdiEEwsLC4OjoCENDQ3To0AEXLlxQKyMrKwvjxo2DtbU1jI2N0atXL9y6detlHwoRERHRC1GtgzkAaNy4MRITE6Xl3Llz0rbw8HAsXLgQy5Ytw/Hjx2Fvb4+uXbvi4cOHUprx48dj27Zt2LRpE/766y88evQIAQEByMvLq4rDISIiIqpUelVdgbLo6empjcYVEEJg8eLFmDFjBvr27QsAWLt2Lezs7LBx40a8++67UKlUWL16NdatW4cuXboAANavXw9nZ2dERUXBz8/vpR4LERERUWWr9iNzly9fhqOjI1xdXfHOO+/g2rVrAID4+HgkJSWhW7duUlp9fX34+voiOjoaABAbG4ucnBy1NI6OjmjSpImUpiRZWVlIT09XW4iIiIiqm2odzLVq1Qo//PAD9uzZg1WrViEpKQk+Pj5ITU1FUlISAMDOzk4tj52dnbQtKSkJCoUCFhYWJaYpybx586BUKqXF2dm5Eo+MiIiIqHJU62DO398fb775Jpo2bYouXbpg586dAJ6eTi0gk8nU8gghiqwrrDxppk2bBpVKJS03b97U8CiIiIiIXpxqHcwVZmxsjKZNm+Ly5cvSdXSFR9iSk5Ol0Tp7e3tkZ2cjLS2txDQl0dfXh5mZmdpCREREVN1oVTCXlZWFuLg4ODg4wNXVFfb29oiMjJS2Z2dn49ChQ/Dx8QEAtGjRAnK5XC1NYmIizp8/L6UhIiIi0mbVejbr5MmT0bNnT9SuXRvJycn49NNPkZ6ejqCgIMhkMowfPx5z586Fm5sb3NzcMHfuXBgZGWHgwIEAAKVSieHDh2PSpEmwsrKCpaUlJk+eLJ22JSIiItJ21TqYu3XrFgYMGIB79+7BxsYGrVu3RkxMDFxcXAAAU6ZMQWZmJsaMGYO0tDS0atUKe/fuhampqVTGokWLoKenh379+iEzMxOdO3fGmjVroKurW1WHRURERFRpZEIIUdWV0Abp6elQKpVQqVQv5Po5Jycn3L59G7Vq1eITKqoRhZkVch7eh9zUEtnpqVVdHSIiqiEqEndo1TVzRERERKSOwRwRERGRFmMwR0RERKTFGMwRERERaTEGc0RERERajMEcERERkRZjMEdERESkxRjMEREREWkxBnNEREREWozBHBEREZEWYzBHREREpMUYzBERERFpMQZzRERERFqMwRwRERGRFmMwR0RERKTFGMwRERERaTEGc0RERERajMEcERERkRZjMEdERESkxRjMEREREWkxBnNEREREWozBHBEREZEWYzBHREREpMUYzBERERFpMQZzRERERFqMwRwRERGRFmMwR0RERKTFGMwRERERaTEGc0RERERajMEcERERkRZjMEdERESkxRjMEREREWkxBnNEREREWozBHBEREZEWYzBHREREpMVqVDC3fPlyuLq6wsDAAC1atMDhw4erukpEREREz6XGBHObN2/G+PHjMWPGDJw6dQrt2rWDv78/bty4UdVVIyIiItJYjQnmFi5ciOHDh2PEiBFo2LAhFi9eDGdnZ3zzzTdVXTUiIiIijelVdQVehuzsbMTGxuKjjz5SW9+tWzdER0cXmycrKwtZWVnSa5VKBQBIT09/IXXMz8+X/n1R+6CKE0IAAHIe3oeeiWUV14aIiF4EmQww1ldUOF//Ye9i/seTXkCN/j/eKPgdKpWoAW7fvi0AiL///ltt/WeffSbq169fbJ7Q0FABgAsXLly4cOHCpcqWmzdvlhnn1IiRuQIymUzttRCiyLoC06ZNw8SJE6XX+fn5uH//PqysrErM8zzS09Ph7OyMmzdvwszMrNLL/y9gG5WO7VM2tlHZ2EalY/uUjW1UuvK2jxACDx8+hKOjY5ll1ohgztraGrq6ukhKSlJbn5ycDDs7u2Lz6OvrQ19fX22dubn5i6qixMzMjJ2/DGyj0rF9ysY2KhvbqHRsn7KxjUpXnvZRKpXlKqtGTIBQKBRo0aIFIiMj1dZHRkbCx8enimpFRERE9PxqxMgcAEycOBGBgYHw8vKCt7c3vv32W9y4cQPvvfdeVVeNiIiISGM1Jpjr378/UlNT8cknnyAxMRFNmjTBrl274OLiUtVVA/D0tG5oaGiRU7v0/9hGpWP7lI1tVDa2UenYPmVjG5XuRbSPTIjyzHklIiIiouqoRlwzR0RERPRfxWCOiIiISIsxmCMiIiLSYgzmiIiIiLQYg7lqYvny5XB1dYWBgQFatGiBw4cPV3WVqo2wsDDIZDK1xd7evqqrVWX+/PNP9OzZE46OjpDJZPj111/VtgshEBYWBkdHRxgaGqJDhw64cOFC1VS2ipTVRsHBwUX6VOvWraumslVg3rx5eO2112BqagpbW1v06dMHly5dUktTk/tRedqnpvehb775Bh4eHtKNb729vfHHH39I22ty/wHKbp/K7j8M5qqBzZs3Y/z48ZgxYwZOnTqFdu3awd/fHzdu3KjqqlUbjRs3RmJiorScO3euqqtUZTIyMtCsWTMsW7as2O3h4eFYuHAhli1bhuPHj8Pe3h5du3bFw4cPX3JNq05ZbQQA3bt3V+tTu3bteok1rFqHDh3C+++/j5iYGERGRiI3NxfdunVDRkaGlKYm96PytA9Qs/uQk5MTPv/8c5w4cQInTpxAp06d0Lt3bylgq8n9Byi7fYBK7j/P9wh7qgwtW7YU7733ntq6Bg0aiI8++qiKalS9hIaGimbNmlV1NaolAGLbtm3S6/z8fGFvby8+//xzad2TJ0+EUqkUK1asqIIaVr3CbSSEEEFBQaJ3795VUp/qKDk5WQAQhw4dEkKwHxVWuH2EYB8qjoWFhfjuu+/Yf0pQ0D5CVH7/4chcFcvOzkZsbCy6deumtr5bt26Ijo6uolpVP5cvX4ajoyNcXV3xzjvv4Nq1a1VdpWopPj4eSUlJav1JX18fvr6+7E+FHDx4ELa2tqhfvz5GjhyJ5OTkqq5SlVGpVAAAS0tLAOxHhRVunwLsQ0/l5eVh06ZNyMjIgLe3N/tPIYXbp0Bl9p8a8wSI6urevXvIy8uDnZ2d2no7OzskJSVVUa2ql1atWuGHH35A/fr1cffuXXz66afw8fHBhQsXYGVlVdXVq1YK+kxx/en69etVUaVqyd/fH2+//TZcXFwQHx+PmTNnolOnToiNja1xd60XQmDixIlo27YtmjRpAoD96FnFtQ/APgQA586dg7e3N548eQITExNs27YNjRo1kgK2mt5/SmofoPL7D4O5akImk6m9FkIUWVdT+fv7S/9v2rQpvL298corr2Dt2rWYOHFiFdas+mJ/Kl3//v2l/zdp0gReXl5wcXHBzp070bdv3yqs2cs3duxYnD17Fn/99VeRbexHJbcP+xDg7u6O06dP48GDB/jll18QFBSEQ4cOSdtrev8pqX0aNWpU6f2Hp1mrmLW1NXR1dYuMwiUnJxf5q4aeMjY2RtOmTXH58uWqrkq1UzDLl/2pYhwcHODi4lLj+tS4cePw+++/48CBA3BycpLWsx89VVL7FKcm9iGFQoF69erBy8sL8+bNQ7NmzbBkyRL2n/8pqX2K87z9h8FcFVMoFGjRogUiIyPV1kdGRsLHx6eKalW9ZWVlIS4uDg4ODlVdlWrH1dUV9vb2av0pOzsbhw4dYn8qRWpqKm7evFlj+pQQAmPHjsXWrVuxf/9+uLq6qm2v6f2orPYpTk3rQ8URQiArK6vG95+SFLRPcZ67/1TaVArS2KZNm4RcLherV68WFy9eFOPHjxfGxsYiISGhqqtWLUyaNEkcPHhQXLt2TcTExIiAgABhampaY9vn4cOH4tSpU+LUqVMCgFi4cKE4deqUuH79uhBCiM8//1wolUqxdetWce7cOTFgwADh4OAg0tPTq7jmL09pbfTw4UMxadIkER0dLeLj48WBAweEt7e3qFWrVo1po9GjRwulUikOHjwoEhMTpeXx48dSmprcj8pqH/YhIaZNmyb+/PNPER8fL86ePSumT58udHR0xN69e4UQNbv/CFF6+7yI/sNgrpr4+uuvhYuLi1AoFKJ58+ZqU+Bruv79+wsHBwchl8uFo6Oj6Nu3r7hw4UJVV6vKHDhwQAAosgQFBQkhnt5WIjQ0VNjb2wt9fX3Rvn17ce7cuaqt9EtWWhs9fvxYdOvWTdjY2Ai5XC5q164tgoKCxI0bN6q62i9NcW0DQEREREhpanI/Kqt92IeEGDZsmPSbZWNjIzp37iwFckLU7P4jROnt8yL6j0wIITQb0yMiIiKiqsZr5oiIiIi0GIM5IiIiIi3GYI6IiIhIizGYIyIiItJiDOaIiIiItBiDOSIiIiItxmCOiIiISIsxmCMiIiLSYgzmiIiIiLQYgzkieqGCg4Mhk8kgk8mgp6eH2rVrY/To0UhLS6vqqmm94OBg9OnTp6qrQURVjMEcEb1w3bt3R2JiIhISEvDdd99h+/btGDNmTFVXiyqREAK5ublVXQ2iGonBHBG9cPr6+rC3t4eTkxO6deuG/v37Y+/evWppIiIi0LBhQxgYGKBBgwZYvny5tC07Oxtjx46Fg4MDDAwMUKdOHcybN0/aLpPJ8M0338Df3x+GhoZwdXXFli1b1Mo/d+4cOnXqBENDQ1hZWWHUqFF49OiRtL1glOvLL7+Eg4MDrKys8P777yMnJ0dKs3z5cri5ucHAwAB2dnZ46623pG1CCISHh6Nu3bowNDREs2bN8PPPP5faLllZWZgyZQqcnZ2hr68PNzc3rF69GgCQl5eH4cOHw9XVFYaGhnB3d8eSJUukvGFhYVi7di1+++03aeTz4MGDAIDbt2+jf//+sLCwgJWVFXr37o2EhAQpb25uLkJCQmBubg4rKytMnToVQUFBaqN8WVlZCAkJga2tLQwMDNC2bVscP35c2n7w4EHIZDLs2bMHXl5e0NfXx7p166Cjo4MTJ06oHefSpUvh4uICPgqc6AURREQvUFBQkOjdu7f0+urVq6JRo0bCzs5OWvftt98KBwcH8csvv4hr166JX375RVhaWoo1a9YIIYSYP3++cHZ2Fn/++adISEgQhw8fFhs3bpTyAxBWVlZi1apV4tKlS+Ljjz8Wurq64uLFi0IIITIyMoSjo6Po27evOHfunNi3b59wdXUVQUFBavU0MzMT7733noiLixPbt28XRkZG4ttvvxVCCHH8+HGhq6srNm7cKBISEsTJkyfFkiVLpPzTp08XDRo0ELt37xZXr14VERERQl9fXxw8eLDEtunXr59wdnYWW7duFVevXhVRUVFi06ZNQgghsrOzxaxZs8SxY8fEtWvXxPr164WRkZHYvHmzEEKIhw8fin79+onu3buLxMREkZiYKLKyskRGRoZwc3MTw4YNE2fPnhUXL14UAwcOFO7u7iIrK0sIIcSnn34qLC0txdatW0VcXJx47733hJmZmdr7FBISIhwdHcWuXbvEhQsXRFBQkLCwsBCpqalCCCEOHDggAAgPDw+xd+9eceXKFXHv3j3RtWtXMWbMGLXj9PT0FLNmzSq9oxCRxhjMEdELFRQUJHR1dYWxsbEwMDAQAAQAsXDhQimNs7OzWnAmhBBz5swR3t7eQgghxo0bJzp16iTy8/OL3QcA8d5776mta9WqlRg9erQQ4mmwaGFhIR49eiRt37lzp9DR0RFJSUlSPV1cXERubq6U5u233xb9+/cXQgjxyy+/CDMzM5Genl5k/48ePRIGBgYiOjpabf3w4cPFgAEDiq3zpUuXBAARGRlZ7PbijBkzRrz55pvS68KBshBCrF69Wri7u6u1VVZWljA0NBR79uwRQghhZ2cn5s+fL23Pzc0VtWvXlsp69OiRkMvlYsOGDVKa7Oxs4ejoKMLDw4UQ/x/M/frrr2r737x5s7CwsBBPnjwRQghx+vRpIZPJRHx8fLmPk4gqhqdZieiF69ixI06fPo2jR49i3Lhx8PPzw7hx4wAAKSkpuHnzJoYPHw4TExNp+fTTT3H16lUAT0+Bnj59Gu7u7ggJCSlyihYAvL29i7yOi4sDAMTFxaFZs2YwNjaWtrdp0wb5+fm4dOmStK5x48bQ1dWVXjs4OCA5ORkA0LVrV7i4uKBu3boIDAzEhg0b8PjxYwDAxYsX8eTJE3Tt2lXtGH744QfpGAo7ffo0dHV14evrW2K7rVixAl5eXrCxsYGJiQlWrVqFGzdulNzQAGJjY3HlyhWYmppK9bC0tMSTJ09w9epVqFQq3L17Fy1btpTy6OrqokWLFtLrq1evIicnB23atJHWyeVytGzZUmrTAl5eXmqv+/TpAz09PWzbtg0A8P3336Njx46oU6dOqfUmIs3pVXUFiOi/z9jYGPXq1QMAfPXVV+jYsSNmz56NOXPmID8/HwCwatUqtGrVSi1fQWDVvHlzxMfH448//kBUVBT69euHLl26lHlNmkwmA/D0eraC/5eUBngasBTeVlA/U1NTnDx5EgcPHsTevXsxa9YshIWF4fjx41KanTt3olatWmpl6OvrF7tfQ0PDUuv+008/YcKECViwYAG8vb1hamqK+fPn4+jRo6Xmy8/PR4sWLbBhw4Yi22xsbNSO7VnimevZCv5fXJrC654NkAFAoVAgMDAQERER6Nu3LzZu3IjFixeXWmciej4cmSOily40NBRffvkl7ty5Azs7O9SqVQvXrl1DvXr11BZXV1cpj5mZGfr3749Vq1Zh8+bN+OWXX3D//n1pe0xMjNo+YmJi0KBBAwBAo0aNcPr0aWRkZEjb//77b+jo6KB+/frlrreenh66dOmC8PBwnD17FgkJCdi/fz8aNWoEfX193Lhxo8gxODs7F1tW06ZNkZ+fj0OHDhW7/fDhw/Dx8cGYMWPg6emJevXqFRnlUygUyMvLU1vXvHlzXL58Gba2tkXqolQqoVQqYWdnh2PHjkl58vLycOrUKel1vXr1oFAo8Ndff0nrcnJycOLECTRs2LDMdhoxYgSioqKwfPly5OTkoG/fvmXmISLNcWSOiF66Dh06oHHjxpg7dy6WLVuGsLAwhISEwMzMDP7+/sjKysKJEyeQlpaGiRMnYtGiRXBwcMCrr74KHR0dbNmyBfb29jA3N5fK3LJlC7y8vNC2bVts2LABx44dk2aGDho0CKGhoQgKCkJYWBhSUlIwbtw4BAYGws7Orlx13rFjB65du4b27dvDwsICu3btQn5+Ptzd3WFqaorJkydjwoQJyM/PR9u2bZGeno7o6GiYmJggKCioSHl16tRBUFAQhg0bhq+++grNmjXD9evXkZycjH79+qFevXr44YcfsGfPHri6umLdunU4fvy4WoBbp04d7NmzB5cuXYKVlRWUSiUGDRqE+fPno3fv3vjkk0/g5OSEGzduYOvWrfjwww/h5OSEcePGYd68eahXrx4aNGiApUuXIi0tTRp1MzY2xujRo/Hhhx/C0tIStWvXRnh4OB4/fozhw4eX2VYNGzZE69atMXXqVAwbNqzMUUgiek5Ve8keEf3XFXeRvhBCbNiwQSgUCnHjxg3p9auvvioUCoWwsLAQ7du3F1u3bhVCPJ3A8OqrrwpjY2NhZmYmOnfuLE6ePCmVBUB8/fXXomvXrkJfX1+4uLiIH3/8UW1/Z8+eFR07dhQGBgbC0tJSjBw5Ujx8+LDUen7wwQfC19dXCCHE4cOHha+vr7CwsBCGhobCw8NDmlkqhBD5+fliyZIlwt3dXcjlcmFjYyP8/PzEoUOHSmybzMxMMWHCBOHg4CAUCoWoV6+e+P7774UQQjx58kQEBwcLpVIpzM3NxejRo8VHH30kmjVrJuVPTk4WXbt2FSYmJgKAOHDggBBCiMTERDFkyBBhbW0t9PX1Rd26dcXIkSOFSqUSQgiRk5Mjxo4dK8zMzISFhYWYOnWqePvtt8U777yjVrdx48ZJZbRp00YcO3ZM2l4wASItLa3YY1u9erUAoJaHiF4MmRC88Q8RaTeZTIZt27bxaQgays/PR8OGDdGvXz/MmTOnUsr87LPPsGnTJpw7d65SyiOikvE0KxFRDXP9+nXs3bsXvr6+yMrKwrJlyxAfH4+BAwc+d9mPHj1CXFwcli5dWmmBIRGVjhMgiIhqGB0dHaxZswavvfYa2rRpg3PnziEqKqpckxvKMnbsWLRt2xa+vr4YNmxYJdSWiMrC06xEREREWowjc0RERERajMEcERERkRZjMEdERESkxRjMEREREWkxBnNEREREWozBHBEREZEWYzBHREREpMUYzBERERFpsf8DxKSDx6iw4NoAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 700x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idata_pps = model.predict(idata=idata, kind=\"response\", inplace=False)\n",
    "\n",
    "bins = np.arange(35)\n",
    "fig, ax = plt.subplots(figsize=(7, 3))\n",
    "ax = plot_ppc_discrete(idata_pps, bins, ax)\n",
    "ax.set_xlabel(\"Response category\")\n",
    "ax.set_ylabel(\"Count\")\n",
    "ax.set_title(\"Sequential model - Posterior Predictive Distribution\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "This notebook demonstrated how to fit cumulative and sequential ordinal regression models using Bambi. Cumulative models focus on modeling the cumulative probabilities of an ordinal outcome variable taking on values up to and including a certain category, whereas a sequential model focuses on modeling the probability that an ordinal outcome variable stops at a particular category, rather than continuing to higher categories. To achieve this, both models assume that the reponse variable originates from a categorization of a latent continuous variable $Z$. However, the cumulative model assumes that there are $K$ thresholds $\\tau_k$ that partition $Z$ into $K+1$ observable, ordered categories of $Y$. The sequential model assumes that for every category $k$ there is a latent continuous variable $Z$ that determines the transition between categories $k$ and $k+1$; thus, a threshold $\\tau$ belongs to each latent process.\n",
    "\n",
    "Cumulative models can be used in situations where the outcome variable is on the Likert scale, and you are interested in understanding the impact of predictors on the probability of reaching or exceeding specific categories. Sequential models are particularly useful when you are interested in understanding the predictors that influence the decision to stop at a specific response level. It's well-suited for analyzing data where categories represent stages, and the focus is on the transitions between these stages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sat May 25 2024\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.11.9\n",
      "IPython version      : 8.24.0\n",
      "\n",
      "bambi     : 0.13.1.dev37+g2a54df76.d20240525\n",
      "arviz     : 0.18.0\n",
      "numpy     : 1.26.4\n",
      "matplotlib: 3.8.4\n",
      "pandas    : 2.2.2\n",
      "\n",
      "Watermark: 2.4.3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:base] *",
   "language": "python",
   "name": "conda-base-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
